Pita, at best, is but a convenient vehicle for something more flavorful. And Peeta Mellark of the Hunger Games is undoubtedly named in honor of this edible homonym. He's a safe, doughy vehicle for Katniss, who is nothing if not full of spice. But lest we think this is just an allegory, allow us to direct your attention to the true subject of this trilogy: hunger. It is, after all, the HUNGER Games. And when you're hungry, maybe you want to snack on some pita. It sure would be more fulfilling than snacking on a Peeta.
In hindsight, who actually realized how often Katniss called for pita? Watch this video as Katniss exclaims, "Oh my god, Peeta," and, "Where's Peeta?" while a pita sandwich is helpfully held in front of the screen, in case you forget which kind of pita/Peeta she truly means.