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 (eye) -> y (why)
MA (Massachusetts) 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 Norse god at his feet, whose kind really starts six places later.
Next is Rand.
First name of Rand al'Thor, someone we are familiar with because they're #1 in Rep here.
Named after the book series, Wheel of Time.
Assuming horse -> Norse, Rand al'Thor
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.
Ir is the end.
Ire - e = Ir, endless anger.
I (9) is half of R (18). And is 3^2 -- one day, from Rubio.
Bonus:
There was a dispute about you posting their rhyme.