I’ll add the caveat that I’m assuming that ‘Fieri’ is the real surname of his ancestors, rather than something he changed it to. Changing it *would* indeed be pretentious, though arguably no more so than the other million celebs that have a stage name.
A “T” is still a “T” and and “R” is still an “R” in any romance language. If you’re talking dialects, well, the guy was born here!
I got curious and looked around, according to Wikipedia he did change his name... it’s really “Ferry.” Of course, that in itself could have been changed when his ancestors immigrated, and he then changed it back, but I’ll go along with “pretentious” for now.