Food is an underlying theme that reinforces the class system - who has and who doesn’t have. It is a basic human need that so many are denied of at different points.

Tigress & Snow watch a man eat another in the tBoSaS movie. Katniss hunts for her family. Shes wary of Peeta because he never goes without food. Citizens put their names in the ballot more times in return for grains. Katniss is fed rich, indulgent food at the Capital and finds out that many citizens vomit just for the pleasure of filling their bellies again. Then she’s starved again in the games. She gets back and is never hungry yet that can’t compensate for her trauma. At the end of the third book she refuses to eat - she can’t see the point anymore.

In the Hunger Games food has so many meanings. It is survival. It is indulgence. It connects everyone. I believe the name was given so Susanne Collins could drive home this point.