Name of God represents the attribute of God. Since a single Name doesn't cover all the attributes of God multiple names are given to cover the attributes of God. Lord Shiva has infinite attributes. Vedas themselves give multiple names to Lord Shiva so that they can cover maximum attributes of Lord Shiva.
Here I have prepared famous names of Lord Shiva which are directly from Vedas. I have also attached commentary of either Lord Krishna or sage Vyasa from Mahabharat to understand meaning of those names. Here are the names:
Shiva is the most famous name which means auspicious. Vajasena Samhita of Yajurveda 3.60 clearly states "Shivo Namaasi Swadhistite" ie. "You are known by the name Shiva. 4.5.8 of Taittariya Samhita of YajurVeda, 16.49 of Vajasena Samhita of YajurVeda gives this name. Lord Krishna states:
Since by all his acts he performs sacrifices for all and seeks the good of every creature, therefore he is called Shiva or the auspicious one. [Anushasana Parva clxi]
It is one of the most popular name. It is stated in Satapatha Brahmana of Yajurveda in 188.8.131.52, Taittariya Aranyaka 10.20.1. Lord Krishna states:
Since he is the foremost of all the deities, and since his dominion and acquisitions are very extensive, and since he protects the extensive universe, therefore he is called Mahadeva. [Anusasana Parva clxi]
Pasupati is another popular name of Lord Shiva. It is stated in several places like T.S.4.5.4,8 ; Satapatha Brahmana 184.108.40.206, Taittariya Aranyaka 10.22.1, T.S. 6.2.3 etc..Vyasa states:
And since he always protecteth the creatures (of the universe) and sporteth with them, and since also he is the lord of all creatures, therefore is he called Pasupati.
[Drona Vadh Parva ccii]
It is another popular name of Lord Shiva. Taittariya Samhita 4.5.8, Vajasena Samhita 16.49 states this name. Shankara means 'One who provides Pleasure'
It denotes fierce aspect of Lord Shiva. It is stated many times like T.S. 4.5.4, Satapatha Brahmana 220.127.116.11 etc.. Lord Krishna states
And since he burneth, since he is fierce, since he is endued with great prowess, and since he devoureth flesh and blood and marrow, he is for this called Rudra. [Anushashana Parva clxi]
This is name of Lord Shiva denoting Lordship. 2.33.9 of Rigveda states 'Isanadasya Bhuvanasya' meaning Lord of World, Satapatha Brahmana 18.104.22.168 and Taittariya Aranyaka 10.21.1 also state this name. Vyasa states:
He that is the embodiment of heaven, earth and sky, the Divine Lord, the protector of the universe, the great Master, the giver of boons, called also Isana. [DronaParva ccii]
This is another popular name meaning cause. It is stated in T.S.4.5.4, Satapatha Brahmana 22.214.171.124. Vyasa states:
And since, he is the Past, the Future, and the Present, and, in fact, everything in the universe, and since he is the origin of the past, the future, and the present, he is for that reason called Bhava. [Drona Parva ccii]
This name is stated in 7.59.12 of Rigveda, 1.8.6.i of Taittriya Samhita, 3.60 of Vajasena Samhita. It means three-eyed. Also means Lord of three world. Vyasa states:
And since three goddesses adore and have recourse to that Lord of the universe, viz., Firmament, Water and Earth, he is for that reason called Tryamvaka. And since Maheswara by means of his two eyes closed (in meditation), created through sheer force of will a third eye on his forehead, he is for that reason called the Three-eyed. [Drona Parva ccii]
This is another popular name of Lord Shiva meaning Great Lord. It is stated in Taittariya Aranyaka of YajurVeda in 10.12.3. It is also stated in Svetasvatara Upanishad 4.10. Ishwara is stated in 10.21 of Taittariya Aranyaka. Mahabharat states this name more than 120 times. Lord Krishna states:
Because he is great (Mahat) and the Supreme Lord of all (Iswara), therefore he is called Maheswara. [Anusasana Parva clxi, Vyasa also states the same in Drona Parva ccii]
Sadashiva which means Eternal Shiva. This name is stated in Taittariya Aranyaka 10.21.1 and Maitreyopanishad 2.6
10.22.1 of Taitariya Aranyaka states Lord Shiva as Umapati and Ambikapati. Uma is consort of Shiva/ Personified Brahma Vidya. Ambika means mother of world. Thus Ambikapati means Lord of mother of World.
This is stated in 4.5.4 of T.S., 126.96.36.199 of Satapatha Brahmana and other places also. Literally it means 'All'. Vyasa states:
He is Yoga and the lord of Yoga; he is called Sarva, and is the Lord of all the worlds. [Drona Parva ccii]
Lord Shiva is also denoted by the name 'Ishwara'. Although it applies for other Gods too. Ishwara is stated in Taittariya Aranyaka 10.21.1 Lord Krishna states:
It is he who is always engaged in all that is
good and evil in the three worlds. In consequence of his fullest control over all objects of enjoyment he is called Ishwara (the Supreme Lord or Master). [Anusasana parva clxi]
It means blue-necked one. It is stated several times. For eg. In Taittariya Samhita 4.5.1. This name is the origin of Popular name Nilakantha.
It means one with matted Hair. This is stated several times. For eg. In Taittariya Samhita 4.5.4
Although Lord Shiva is more populary known as Mahakaal as his consort is Mahakali. 'Kala' name which means 'who is time' is stated in Taittariya Aranyaka 10.18.1
Tripurari means destroyer of three cities made by Asuras. So, Lord Shiva is Tripurantaka. Name got from story of Taittariya Samhita of YajurVeda 6.2.3.
Sithikantha meaning white throated one. It denotes the white colour of ash around Lord Shivas name. This name is frequently used in Sri Rudram part of YajurVeda like in Taittariya Samhita 4.5.4.
There are other Several Names like
Ugra [Satapatha Brahmana 188.8.131.52]= meaning fierce
Bhima [T.S. 4.5.7]=meaning giant
Aghora [T.A. 10.19.1]=meaning Benign
Bhutanamadhipati [V.S. 16.48] = meaning Lord of all beings.
Vamadeva [Taittariya Aranyaka 10.18.1],
Virupakshya [Taittariya Aranyaka 10.22.1]=meaning having uncommon(odd) eyes and other names too denoting infinite Attributes of Lord Shiva.
Note: here, T.S. =Taittariya Samhita of YajurVeda, V.S. = Vajasena Samhita of YajurVeda, T.A.= Taittariya Aranyaka of YajurVeda.