Not Hungarian native but, ez and Péter are both either pronouns or holders for pronouns therefore the Hungarian language doesn't need a form of "to be", whereas in the sentence "Mi bent" there is no pronoun, so a form of to be is needed to identify a person/object.
Except "what is in" is not a grammatical sentence - "in" needs an object. "Belül" means something slightly different, but I'm having trouble articulating it.