It's Mithrandir
His head sounds like a myth, with an eye for why
Endless, it says to meet but briefly so,
standing for the very famous MA institute.
Mith is the head, sounds like Myth also i -> y
MA Institute -> MIT, front of Mithrandir
Then comes the first name of another puzzler, we all are very familiar with
named after the prime of a time wheel with
a horse god at his feet, whose kind really starts six places later.
At last, anger or annoy without end—
its birth is half the death, where the dawn is equally four sided of
any trio’s total member number.
Bonus:
There was a dispute about you posting their rhyme.