If Eva a neved is correct so should Péter a neved be correct.
Is this really correct: "Péter a te neved"? It's listed as a possible response.
Can the subject pronoun really come between an article and the noun it's making (in)definite, like adjectives can?
It can, to give emphasis. In a kiddies' story I'm reading the grandmother tells the little girl about "az én nagymamám" = "my grandmother"
Thanks for the confirmation.