Yes, 'Koti' means 'a class' according to :http://sanskritdictionary.com/?iencoding=iast&q=कोटि&lang=sans&action=Search
As per the Satapatha Brahmana
kathamete trayatrimsad iti astau vasavah ekaadasha rudra dwadasa-aadityaastu ekatrimsad indraischa prajapatisch atryastrimsad iti
meaning : thirtythree types of devas are eight vasus, eleven rudras, twelve adityas, Indra and Prajapati. (Reference :Pranava-Prema-Pijusha-Bhashya of Gita, Sitaramdas Omkarnath, page 101-102).
Vasus: Agni, prithivi, vayu, antariksha, aditya,swarga,chandramaa,nakshatraloka.
vasayanti viswam : They keep the world dwelling('vaasa') and so they are called vasu. (Ibid, page 101)
Tweve Adityas are the twelve months. (Ibid page 101).
According to Srimad-Bhagavatam, they are names of twelve Suns in the twelve months:
Vishnu (The head of all the Adityas)
As Indra, Surya destroys the enemies of the gods. As Dhata, he creates living beings. As Parjanya, he showers down rain. As Tvashta, he lives in the trees and herbs. As Pusha, he makes foodgrains grow. As Aryama, he is in the wind. As Bhaga, he is in the body of all living beings. As Vivasvana, he is in fire and helps to cook food. As Vishnu, he destroys the enemies of the gods. As Amshumana, he is again in the wind. As Varuna, he is in the waters and As Mitra, he is in the moon and in the oceans. (source : wikipedia).
Eleven Rudras are
Nirriti,Shambhu,Aparajita,Mrigavyadha,Kapardi,Dahana,Khara,Ahirabradhya,Kapali,Pingala,Senani (Matsya-Purana). There are different names in different Puranas, available on Wikipedia.
Another opinion is that
sotra, twak,chakshur, jihva,ghrana,vak,pani,pada, payu,upastha, praana and manas are the eleven Rudras. "tat tat rodayati iti rudrah" --they make others weep when they go out of a mortal body and so they are called Rudra.(Ibid page 102)
Another view is 'Brahmaa-anurodhena kritajanmaparigraho ruditabaan iti rudrah: They took birth on Brahma's request and cried and so are called Rudras (Ibid vol 2 page 10)
Indra means the samastaad vyaapta taridshakti,(the all pervading electricity-energy), vala and virya of all living beings.(Ibid page 102)
Prajapati is Yajna, as from Yajna the creation, sustenance and destruction of the world happens.(Ibid page 102)
There are slight variations in the names of the Rudras.
Reference : http://creative.sulekha.com/the-rudras-eleven_398301_blog
The earliest mentions of Rudra occur in the Rig Veda, where three entire hymns are devoted to him.
Rig Veda mentions a set of thirty-three deities. According to Yaska-charya, the thirty-three gods are divided equally in three different planes of existence namely the celestial plane (dyuloka) the intermediate region (antarikshaloka) and the terrestrial region (bhurloka) each plane having eleven gods.
There is however a slight variation among the different traditions in naming the thirty-three deities. According to the Shatapatha Brahmana, these thirty-three deities include eight Vasus, eleven Rudras, twelve Adityas, Dyaus, and Prithvi. While, Yaska-charya mentions: eight Vasus, eleven Rudras, twelve Adityas and two Asvinis.
In the Brihadaranyaka Upanishad the Rishi Yajnavalkya at one stage says “The eight Vasus, eleven Rudras, twelve Adityas, Indra and Prajapati are the thirty-three gods".
He goes on to explain: Katame rudra iti: "Who are the Rudras?" and says "The ten senses and the mind make eleven. These are the Rudras.""When the senses and the mind leave the body, they make one cry in anguish." While a person is alive, these eleven: the senses and the mind, subject the individual to their demands, and make him cry in agony if he violates their laws.
In Rig Veda, Rudra is one of the intermediate level gods (antariksha devata) .He is described as fierce, armed with bow and fast-flying arrows , ‘brilliant shafts which run about the heaven and the earth’ (RV 7.46.3). He is endowed with strong arms, lustrous body decorated with ornaments and having flowing golden hair.
Rudra is a divinity of the subtle world, the sphere of space, the mid sphere between the earth and the Sun (Rig Veda 5.3). Rudra is thus a deity of the intermediate stage. He presides over the second ritual of sacrifice, the mid-day offering, the second period of man’s life (say from 24to 50).
Rudra is the intermediary between physical elements and the intellect, between the spheres of earth and the Sun. Rudra (the howling one) as a divinity associated with winds represents life-breath (prana-vayu).Rudra is thus the principles of life.
Rudra the howler or the red one is the cause of tears, because : ”verily, the vital breaths are the cause of the tears, for on departing they cause everyone to lament in tears” (Chandogya Upanishad 3.16.9).
Rudra is also regarded as the best physician- bhishaja shiromani-Vaidyanatha (RV 2.33.4). He is said to have healing remedies (RV 1.43.4), and thousand medicines (RV 7.46.3). “Do thou with strengthening balms incite our heroes”. He is asked not to afflict children, men and cattle with disease (RV 7.46.2) and to keep villages free of illness (RV 1.114.1).
He is "fierce like a formidable wild beast" (RV 2.33.11). He is not purely benefic like other Rig Vedic gods, but he is not malevolent either. Rudra is thus regarded with a kind of cringing fear and respect .He punishes and at the same time he rescues his devotees from trouble. One appeals to "mighty Rudra, the god with braided hair” for mercy and protection (RV 1.114).
He is also Shiva the auspicious one. He is known for his wealth. He is also associated with Aditya (sun) and Agni. He is addressed as the thousand-eyed one (saharaksha) holding thunderbolts. He is associated with the dramatic fierceness of the thunderstorm and lightening which strike at men and cattle, but which through the rain brings forth peace and plenty.
He is the father of Maruts the "storm gods"; hence they are called Rudriya. They are the deities who bring havoc, associated with the atmosphere The Maruts (immortals) are described as restless troops of flashy young men, transporting in space the hordes young warriors called maryus (mortals).
Maruts are war-minded close knit bunch of exuberant youth. “They have iron teeth, roam like lions, hold bows and arrows and round projectiles; they speed away in golden chariots drawn by tawny stallions. They dwell in the North.”(RV 1.153.6).
Riding on the whirlwinds, singing loudly, they direct the storms. Clad in rain, they spread rain, pushing away storm. When they move the mountains tremble and trees fall (RV 1.39.5; 5.53-54)
They are known for moral and heroic deeds. Often brutal, though usually good humoured, they are feared by everyone.
The number of Maruts varies. They are a group of gods, supposed to number usually either eleven or thirty-three. The Rig Veda speaks of them as twenty-one (RV 1.133.6) as twenty-seven or forty-nine (seven groups of seven each) or one hundred and eighty (three times sixty in RV 8.96.8.).
The Rig Veda sings the glory and splendour of the Rudra:
Chief of all born art thou in glory, Rudra, armed with the thunder, mightiest of the mighty (2.33.03)
To him the strong, great, tawny (Bhabru Varna), fair-complexioned, I utter forth a mighty hymn of praises. We serve the brilliant God with adorations, we glorify, the splendid name of Rudra.(2.33.08)
With firm limbs, multiform, the strong, the tawny adorns himself with bright gold decorations: The strength of Godhead never departs from Rudra, him who is Sovereign of this world, the mighty.(2.33.09)
Worthy, thou carry thy bow and arrows, worthy, thy many hued and honoured necklaces.
Worthy, thou cut here each fiend to pieces: a mightier than thou there is not, Rudra.(2.33. 10)
Praise him the chariot-borne, the young, the famous, fierce, slaying like a dread beast of the forest (2.33.11).
In Rig Veda, as it is often said, the term Shiva occurs eighteen times. And, each time it is used as an adjective, an epithet standing for “an auspicious one” (mangalakara) in the sense of being “propitious" or "kind" (10.92.9).Shiva, in Rig Veda, is not the name of any god. It is a quality found in many gods.
Rudra, on the other hand, is not merely the proper name of a deity; but it also is one that refers to a collection of Rudras. Even among his collective forms, he has twin aspects: his terrible aspects as well as his benevolent aspects (dve tanu tasya devasya).Rudra is a fierce deity of stormy winds, deafening thunderbolts, devastating floods and raging epidemics. Rudra is also benevolent; he is wealthy; he reassures the frightened ones and cures deceases.
Oh, the devoted to the devotees, always travelling in the chariot, ever young, fierce like the lion, vanquisher of the enemies, May the devotees pray to you. May you make us happy. May your armies fight against the enemies and be merciful towards us. There is none that matches him in strength. He is the Ishana the Master of the world; he is the father of worlds (Bhuvanasya pitaram).He commands men and entrusts tasks. He sets things in motion and makes flow like a river. He is medhavi, intelligent and the compassionate one. He is praised as midvah, for his generosity. As he is an auspicious one, he is called Shiva. (RV: 2-33-7; 6-49-10; 7-46-2)
Stomam vo adya rudraya shikvase..Kshaatadiraya namasa didistana... Yebhih Shivah svavam yevayabhihi ... Divaha sishakti svayasha nikamabhihi..|| (RV: 10-92-9)
It is said, that Rudra’s identification with Shiva came much later; and for the first time in Svetavatara Upanishad and later in Yujurveda (Taittariya samhita, 4-5-1 – shatarudriya section). Vajaseniya samhita (3-63) also identified Shiva with Rudra (tam Shiva namasi). Shathapatha Brahmana too said Shiva was known as Bhava, Mahadeva, Sarva, Pashupathi, Ugra and Ishana. Panini (say 4th century BCE) in his Grammar -Astadhyayi (1-49; 3-53; 4-100; 5-3-99) mentions that Rudra was called variously: Mrida, Bhava, Sarva, Grisha, Mahadeva and Trayambaka.
Patanjali (in Mahabashya) also mentions icons of Shiva along with those of Skanda and Visakha. By Patanjali’s time (say 2nd or 3rd century BCE), I reckon, Shiva as god with his attributes was well established.
By the time of the Puranas, Rudra came to be completely equated with Shiva who is one of the Trinity and is represented as the destroyer. Not surprisingly, Rudra is closely associated with the god of death, Yama; with the god of fire, Agni; and with the magical drink, soma. He is also an aspect of Shiva the Lord of the universe, the cosmic dancer, the Supreme yogi and master of all yogis.
In Rudra Prashna
In the Shata-rudriya, or the hundred names of Rudra, or the famous Namaka hymn of Rudra Prashna found in the Vajasaneyi samhita of Yajurveda:
" Rudra is described as possessing many contradictory attributes; for example, he is a killer and destroyer; he is terrible, fierce ( ugra), inauspicious ; he is a deliverer and saviour; he causes happiness, and prevents disease ; he has a healing and auspicious body (siva tanuh); he is yellow-haired, brown- coloured, copper-coloured, ruddy, tall, dwarfish; he has braided locks (kapardin), wears the sacred thread, and is clothed in a skin ; he is blue-necked and thousand-eyed; he dwells in the mountains, and is the owner of troops (gana-pati) of servants who traverse the earth obeying his orders ; he is ruler and controller of a thousand Rudras who are described as fierce and ill-formed (virupa); he has a hundred bows and a thousand quivers; he is the general of vast armies; he is lord of ghosts, goblins, and spirits; of beasts, horses, and dogs; of trees, shrubs, and plants; he causes the fall of leaves ; he is lord of the Soma-juice; he is patron of thieves and robbers, and is himself present in a thief, robber, and deceiver; he presides over carpenters, chariot-makers, blacksmiths, architects, huntsmen; he is present in towns and houses, in rivers and lakes, in woods and roads, in clouds and rain, in sunshine and lightning, in wind and storm, in stones, dust, and earth."
- -Monier-Williams (of the Boden Chair of Sanskrit at Oxford University)
The myths and legends that allege the origin of the Rudra abound. There are a variety of stories. I do not propose to discuss them here. Suffice it to say, all those legends have in common the Shiva, anger, howling or crying out loud.
The etymology of the word Rudra is interpreted variously; and at times is confusing. Its etymology has taken scholars into all sorts of wild chase.
Rudra in Rig-Veda is a god of the storm, the wind, and the hunt. His distinctive characteristics are his fierce weapons and his medicinal powers. He is the ‘archer’(sarva - sarv - which means ‘to injure’ or ‘to kill’), the ‘bowman’ (dhanvin) armed with fast-flying arrows (ashu - bana-hastha).
The name Rudra has been translated as ‘roarer’, ‘howler’, ‘wild one’, ‘the fierce god’ and ‘terrible’. The alternate etymology suggested as derived from the root rud is: ‘to be Red, Brilliant’, ‘to be ruddy’ or ‘to shine’. Rudra is sometimes identified with the god of fire-Agni.
Rudra is also used both as a name of Shiva, synonymous with Bhava, Sarva, Ugra and Mahadeva.
Rudra also means ‘Father of the Maruts’(RV 2.33.1); and collectively "the Rudras" is used to mean ‘the sons of Rudra’ or the Maruts.
According to a commentary on Vishnu Sahasranama (ascribed to Sri Sankara) , Rudra means ‘One who makes all beings cry at the time of cosmic dissolution’. Alternatively, Rudra means ‘One who gives speech’. Rudra also means ‘one who drives away sorrows’.
The Rudras are said to be truly infinite (shatam anantam bhavati, asankhyakam). They are present everywhere, manifest in millions of forms in as many abodes; and influence every aspect of creation (sahasrani sahasrasho ye rudra adhi bhumyam...); and they are there even in the food we eat and drink we consume (ye anneshu vividhyanti prateshu pibato janan...). They are immanent within us. They are the protectors of the beings and the created world; the decay and destruction sets in when they refuse to support. Pray therefore to the Rudras for protection and benevolence; and to alleviate our troubles. (Shata rudriyam- Rudra prashna).
The Rudras are however talked in terms of sets of eleven- Ekadasa Rudra, inasmuch as the term Rudra has virtually come to represent ‘the number eleven’. However, each tradition, each text has its own set of eleven Rudras, according to its priorities. Their names and attributes differ from one text to another. There is thus, virtually, a plethora of Rudras. But, each of them represents a certain aspect of Shiva or Rudra.
The following are some instances of the names of the eleven Rudras according to different authorities:
: Shatarudriya hymns celebrates Rudra in his eleven forms as : Aghora (benevolent); Kapardi (with matted hair); Girisha (Lord of mountains) ; Bhima( terrible) ; Nilagriva (blue throated); Trayambaka (three eyed); Sabhapathi (master of the assembly); Ganapathi (leader of the hosts); Senani(commander of forces); Samkara(doer of good ); and Shambhu (appearing for the welfare of all).
: Rudra Prasna (3.5): Bhava; Sharva; Pashupathi; Nilagriva; Shithikanta; Kapardina; Vyupta-kesha; Shasraksha; Shatadhanva; Girisha ; and Shipivista.
: Rupa-mandana (a text of Shilpa sastra) : Isana; Tatpurusha; Aghora; Vamadeva; Sadyojatha; Mruthyunjaya; Kiranaksha;Srikanta;Abhirbhudhya;Bahurupa; and Tryamkaka.
: Visvakarma Shilpa (a text of Shilpa sastra): Aja; Ekapat; Abhirbudhya; Virupaksha; Revata; Hara; Bahurupa; Tryambaka; Suresvara; Jayanta; and Aparajita.
: Amsumad bheda agama ( a text of Shilpa sastra): Mahadeva; Siva; Rudra ;Sankara; Nilalohita; Isana; Vijaya; Bhima; Deva -Deva; Bhava ; and Kapali.
: Padma Purana: Rta-dhvaja; Manu; Manyu; Ugra-retas; Mahan; Siva; Bhava; Kala; Mahinasa; Vamadeva; and Dhrta-vrata.
: Mahabharata (Adi Parva): Mrigavyadha; Sarpa; Niriti; Ajaikapat ; Abhivardhana ; Pinaki ; Dahana ; Iswara ;Kapali ;Sthanu ;and Bharga.
: Valmiki Ramayana (4.43): Aja; Ekapada; Abhirbhudya; Hara; Shambu: Tryambaka; Aparajita; Isana; Tribhuvana; Twasta; and Rudra.
: Srimad Bhagavata (3.12.12):Manyu ; Manu; Mahinasa; Mahan; Siva; Rta-dhvaja; Ugra-reta; Bhava; Kala; Vamadeva; and Dhrta-vrata.
: Agni Purana (Ch 18) :Aparajita; Hara; Bahurupa; Tryambaka; Vrsakapi; Shambu; Kapardina; Raivata; Mriga vyadha; Sarpa; and Kapali.
: According to Jothish Sastras (Astrology ) : Kapali; Pingala; Bhima; Virupaksha;Vilohita; Shasta; Ajapada; Abhirbudhnya; Shambu; Chanda ;and Bhava.
According to Aaitareya Brahmana(2/4), Indra is replaced by Vasatkarah (Ibid page 101).