To my knowledge, Suzanne Collins has never definitively stated this either way.
However, the fan consensus is that Peeta's name is a reference to the fact that he comes from a family of bakers. In addition to the homonym, Peeta's name may also be a reference to his following of another - as did Peter, the apostle.
Peeta Mellark (Josh Hutcherson: Katniss’ fellow District 12 tribute comes from a family of bread bakers, and his name is an alternate—or dystopic, if you will—spelling of pita. The humble Peeta stands in contrast to the grandiose Panem, which, as noted above, is Latin for bread. Commenters have also pointed out that Peeta is very similar to Peter—and while Hunger names are not generally Biblical, Peeta is, like that apostle, the closest friend to the savior (Katniss), and does everything he can for her.