Do you think Collins put "The Hunger Games" as a title on purpose to describe Katniss' district? How do you think this effects Katniss as her character?

I think the title Hunger Games works on a literal and figurative level. Literally the Hunger Games is an exploitive display by Panem to remind the districts how much power they have. Figuratively, these "games" represent the poverty and starvation the districts must endure every day just to survive. People in the districts must be clever, strong, and show ingenuity just to survive their daily lives.