As defined in the Purans:

Vasudeva said: O mighty armed Yudhishthira, listen to me as I recite to thee the many names of Rudra as also the high blessedness of that high-souled one. The Rishis describe Mahadeva as Agni, and Sthanu, and Maheswara; as one-eyed, and three eyed, of universal form, and Shiva or highly auspicious.

Brahmanas conversant with the Vedas say that Siva has two forms. One of these is terrible, and the other mild and auspicious. Those two forms again, are subdivided into many forms. That form which is fierce and terrible is regarded as identical with Agni and Lightning and Surya (fire, lightning and sun).

The other form which is mild and auspicious is identical with Righteousness and Water and Chandramas (moon).Then again, it is said that half his body is fire and half is Soma (or the moon). That form of his which is mild and auspicious is said to be engaged in the practice of the Brahmacharya (Celibacy) vow. The other form of his which is supremely terrible is engaged in all operations of destructions in the universe.

Because he is great (Mahat) and the Supreme Lord of all (Iswara), therefore he is called Maheswara. And since he burns and oppresses, is keen and fierce, and endued with great energy, and is engaged in eating flesh and blood and marow, he is said to be Rudra.

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.

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.

Staying above (in the sky) he burns the lives of all creatures and is, besides, fixed in a particular route from which he does not deviate. His emblem, again, is fixed and immovable for all time. He is, for these reasons, called Sthanu. He is also of multiform aspect. He is present, past and future. He is mobile and immobile. For this he is called Vahurupa (of multiform aspect).

The deities called Viswedevas reside in his body. He is, for this, called Viswarupa (of universal form). He is thousand-eyed; or he is myriad-eyed; or, he has eyes on all sides and on every part of his body. His energy issues through his eyes. There is no end of his eyes.

Since he nourishes all creatures and sports also with them, and since he is their lord and master, therefore he is called Pashupati (the lord of all creatures).

Since Mahadeva becomes highly gratified with the worshipper. Affectionate towards his devotees, he bestows happiness upon them with a cheerful soul.

This great god loves to reside in crematoria and there he burns and consumes all corpses. Those persons that perform sacrifices on such grounds attain at the end to those regions which have been set apart for heroes. Employed in his legitimate function, he it is that is regarded as the Death that resides in the bodies of all creatures.

That righteous-souled deity, ever willing to grant protection to all, Long life, health and freedom from disease, affluence, wealth, diverse kinds of pleasures and enjoyments, are conferred by him, and it is he also who snatches them away.

Since, again, he is the master of the vast universe, he is called Maheswara. The whole universe is pervaded by him in diverse forms.