Do Vedas describe about the 11 rudras?
What are the names of those rudras according to Vedas?
How did they emerge from the supreme Rudra?
No, they are not 11 Rudras mentioned in the Vedas. This is a concept invented in the Puranas. Specifically, Matsya(५.२९-३॰), (Harivamśa (१.३.४९-५२) and has no support in the Vedas.
Rig Veda reveals Rudra as श्वितीचे (śvitīce) (२.३३.८) which is translated by Sāyaṇa as of white complexion.
He is one among two or three gods who are invoked as having or assuming all forms. Another epithet for Rudra is varāha (१.११४.५) दिवो वराहमरुषं कपर्दिनं त्वेषं रूपं नमसा नि ह्वयामहे which is explained by Sāyaṇa one who has good food.
Rudra bestows happiness on the sons and grandsons of the invoker (२.३३.१४) परि णो हेती रुद्रस्य वृज्याः परि त्वेषस्य दुर्मतिर्मही गात् ।अव स्थिरा मघवद्भ्यस्तनुष्व मीढ्वस्तोकाय तनयाय मृळ and grants a longer life and progeny (२.३३.१-२) अभि नो वीरो अर्वति क्षमेत प्र जायेमहि रुद्र प्रजाभिः
Another important aspect of Rudra is his power to heal.
Prayers are presented to Rudra to provide medicines (२.३३.१२) कुमारश्चित्पितरं वन्दमानं प्रति नानाम रुद्रोपयन्तम् । भूरेर्दातारं सत्पतिं गृणीषे स्तुतस्त्वं भेषजा रास्यस्मे and he is the Chief among all the physicians (२.३३.४ and १.११४.१). मा त्वा रुद्र चुक्रुधामा नमोभिर्मा दुष्टुती वृषभ मा सहूती । उन्नो वीराँ अर्पय भेषजेभिर्भिषक्तमं त्वा भिषजां शृणोमि ॥४॥
Rudra is described as the Lord of the world (२.३३.३-४) श्रेष्ठो जातस्य रुद्र श्रियासि and nobody is possessing more power than him (२.३३.१॰). अर्हन्निदं दयसे विश्वमभ्वं न वा ओजीयो रुद्र त्वदस्ति
In Rig Veda Rudras were mentioned as Maruts.
Rig Veda I.39 was dedicated to Maruts.
नहि वः शत्रुर विविदे अधि दयवि न भूम्यां रिशादसः |
युष्माकम अस्तु तविषी तना युजा रुद्रासो नू चिद आध्र्षे || Rig Veda I.39.4
Consumers of your foes, no enemy of yours is found in heaven or on the earth: Ye Rudras, may the strength, held in this bond, be yours, to bid defiance even now.
And, Maruts were mentioned as the children of Rudra and Pṛśni (Rig veda VI.66.3)
They who are Sons of the rain-pouring Rudra, whom the long-lasting One had power to foster: The Mighty Ones whose germ great Mother Pṛśni is known to have received for man's advantage.
According the Wikipedia article, the number of Marutas varies from 27 to sixty .
They are very violent and aggressive, described as armed with golden weapons i.e. lightning and thunderbolts, as having iron teeth and roaring like lions, as residing in the north, as riding in golden chariots drawn by ruddy horses.
Here is how Vedas count Rudras:
- The diversity in counting Rudras is taken into consideration during the Yajñá in the discussion. For example, Kṛṣṇa Yajur Vedā Taittirīya Saṃhitā 1.4.11 states “three and thirty in troops”; at the same time it says “eleven are seated on waters”.
- When Vedic meter is considered, Rudras are associated with Triṣṭubh which has 11 syllables multiplied by 4 steps, hence Śrī Rudram of the Kṛṣṇa Yajur Vedā describes 11 homages to Rudra.
- Similarly, Śatarudriya of the Sukla Yajur Vedā mentions 6 Rudras with Triṣṭubh and gives 6 X 11 = 66 homages to 100 Rudras. The same Śatarudriya 16.54 states that Rudra manifests in all and so there are innumerable thousands of Rudras.
- Yoga of Ṛṣi Vaśiṣṭha describes 100 Rudras, whereas the Mahabharata Itihāsa in its Drona Parva-Narayanastra-mokshana Parva 203 says “Infinite Rudras”.
- When offering of sacrifice during Yajñá is in the discussion, Atharva Veda 15.5 talks about 7 intermediator/intermediate spaces in different directions – Bhāva to the Eastern, Śarvā to Southern, Paśūpati to Western, Ugra/Aghora to Northern, Rudra towards nadir or below regions, Mahādeva to the upper regions of the sky/zenith and īśhana towards all directions.
- When associated with the human body, Sharva (Śarvā) is associated with the kidneys, Bhāva with the liver, Rudra with the blood and the liver, Paśūpati and Agni with the heart, Mahadeva with the intestines and Ugra/Aghora with the stomach/gut TS1.4.36.
- Vājasaneyi Saṃhitā of the Sukla Yajur Vedā describes 6 aspects – Bhāva, Rudra, Śarvā, Paśūpati, Nilagriva and Śitikaṇṭha.
- When Rudra is associated with Liṅga then five aspects are described – Sadyojata, Vamadeva, Aghora, Tatpurusha and īśhana.
- Rishi Yagnavalkya in Brihadaranyaka Upanishad, attributes the 10 vayus (prânas), and 11th as the Âtman are all Rudras.Various Anuvākam with their respective meters/syllables make up the mantra, using which various manifestations of Rudras are appeased in Yajñá. For example, Virād meter is of 10 syllables used to give oblation in 10 directions to 10 prāṇas which provide full life called āyus.
- Taittirīya Saṃhitā 4.5 talks about 1000 Rudras covering the Earth with 100 bows and 100 arrows.
So, here is the key: depending on the cause and the event, the concept of Rudra manifests. This is the reason why He is called Viṣvarūpam or Pururūpam (the universal or cosmic form with multiple flavors) RV 2.33.10/TA 10.23.1. Śrī Rudram and Śatarudriya presents totality of Rudra’s omnipresence (which we will explore soon) – especially Taittirīya Saṃhitā 1.8.6, which says “एक एव रुद्र न द्वितीयाय तस्थुर्” meaning “There is only One, Rudra without a second”. This, in turn, gave a foundation to the Svetasvatara Upaniṣhad (one among the 18 primary Upaniṣhads), which says in Chap 3, sloka 2. However, when it’s common for human intellect to iconify names like Rudra and limit such name with an image, but we saw how Rudra is not a person or a creature or to be limited to an iconification, so what better than Chandogya Upaniṣhad Chap 6:
एको हि रुद्रो न द्वितीयाय तस्थुर्य इमांल्लोकानीशत ईशनीभिः। प्रत्यङ्जनांस्तिष्ठति सञ्चुकोचान्तकाले संसृज्य विश्वा भुवनानि गोपाः॥ There is (हि) The One (एको ) Rudrā (रुद्रो) and none (न) other than He, none can make Him second (द्विती) in being (याय) that is in existence (तस्थु:र्य) among the worlds( इमां:ल्लोका), He is the authority (ईशते) by His own authority (ईशनीभिः)| In all worlds/dimensions (भुवनानि) is His convolution and projection and guardians (संसृज् + ज्य + गोपाः) in entirety (विश्वा), He is established (तिष्ठति) in all beings (हे जनाः) as the indweller (प्रत्यङ्); and all beings (भूत्वा), at the time of final dissolution (अन्त:काले), become/withdraw into Him (सञ्चुकोच) ~ Svetasvatara Upaniṣhad 3.2
सदेव सोम्येदमग्र आसीदेकमेवाद्वितीयम् । तद्धैक आहुरसदेवेदमग्र आसीदेकमेवाद्वितीयं तस्मादसतः सज्जायत ॥6.2.1 कुतस्तु खलु सोम्यैवंस्यादिति होवाच कथमसतः सज्जायेतेति। सत्त्वेव सोम्येदमग्र आसीदेकमेवाद्वितीयम् ॥ 6.2.2 यथा सोम्य मधु मधुकृतो निस्तिष्ठन्ति नानात्ययानां वृक्षाणांरसान्समवहारमेकतांरसं गमयन्ति ॥ 6.9.1 ते यथा तत्र न विवेकं लभन्तेऽमुष्याहं वृक्षस्य रसोऽस्म्यमुष्याहं वृक्षस्य रसोऽस्मीत्येवमेव खलु सोम्येमाः सर्वाः प्रजाः सति सम्पद्य न विदुः सति सम्पद्यामह इति ॥ “from a single ball of clay, we can know every form made of clay, the difference in form is but the name (nama-rūpa). In the beginning was one being, without a second, or non-being, without a second; and from that various beings came to be. Just like bees make one honey from nectars of various flowers, yet the honey do not know from which tree or flower, in the same way, all beings begotten from One Being do not know their source” Please note: the word “Being” doesn’t mean a person nor an alien or animal, beings means “to be” or “to exist”. Existence can’t be described or iconified with in image/form within the frontier of vocabulary. ~ Chandogya Upaniṣhad 6.2.1/6.2.2/6.9.1/6.9.2
For more detailed information please google "Sanatanadhara Siva Rudra across Vedas and Itihasa"