I don't pronounce them the same at all. Are you British? I know British people who pronounce it the same.
Peeta is like the group
PETA. pee-tah
Peter is pee-ter.
Finnick is not a good name. Finicky means to be fussy about something so that's all I think of. I like
Finn.
Finn >
Finley >
Finlay