Are there different names to refer to Shiva, depending on the connotation?

I mean, for instance, the story of Daksha seems to me to involve Shiva as a man. The story about Shiva opening his Third Eye and destroying one of the five heads of Brahma is obviously metaphysical, involving divine beings.

So, is the word "Isha" the first name of Adiyogi? And is Adiyogi considered Shiva himself : God who came to teach to humans?