Question

Why is Polyphemus so humiliated when Odysseus reveals his name?

not what he thought his name was btw so the answer is not "nobody"

Answer 1

Odysseus tried to trick Polyphemus by saying his name is Nohbdy as in nobody and the cyclop being dumb fell for it hence he was humiliated

Answer 2

Because he sounded foolish and his neighbors couldn’t help him, since he was tricked by Odysseus