When Katniss destroyed the food stocks of career tributes, she got amused on the idea of the game being The Real Hunger Game because career tributes weren't good at hunting. If the game wasn't real hunger game otherwise, why was it named that way?
Note: I am asking from in-universe perspective obviously.
I would like to expand on the panem et circenses quote. For this question I am drawn to this because "Hunger Games" and the quote are very similar as they both refer to using food and entertainment as means of control.
There is a dialogue in Mockingjay, chapter 16 which I think supports my view:
..., whereas in the Capitol, all they have known is Panem et Circenses"
"What's that?" I recognize Panem, of course, but the rest is nonsense"
"It's a saying from thousands of years ago, written in a language called Latin about a place called Rome," he explains. "Panem et circenses translates into 'Bread and Circuses.' The writer was saying that in return for full bellies and entertainment, his people had given up their political responsabilities and therefore their power.
I think about the Capitol. The excess of food. And the ultimate entertainment. The Hunger Games. "So that's what the districts are for. To provide the bread and circuses."
This explains the idea behind the Hunger Games.
However about the calling it "Hunger" I was not able to find a reference. My personal interpretation is that Hunger refers to inhabitants of the districts as opposed to well fed Capitols. Also similar to Gladiators which also were not citizen. I think there were quotes where Capitols looked down on people from districts as primitives who were obsessed/concerned with food - while in the Capitol they concentrated on "civilised" matters like arts, fashion and such.
Out of universe interpretations point out that Hunger Games may be a play on the original quote. It might actually be a strategy to keep the districts hungry and keep the disengaged only through the games. As the games also created rivalry between the districts this might also be reasonable.
The Games are not about Tributes competing for food; they are about Tributes-as-District-avatars competing for resources (...including food).
You should read Emrah Peksoy's Food as control in the Hunger Games, of which the following quote sums it up nicely:
The Capitol [exercises control] by withholding food to prove its dominance in the districts and by distributing it freely to keep the citizens in the Capitol satisfied
The "Hunger Games" are merely the crowning piece of a society in which feast and famine are used to control the districts and their people:
panem et circenseswhich translates to "bread and games". In context this was a recipe to keep people from engaging in politics. However why call the games hunger games and the capital panem (=bread) - must be a more convoluted train of thought. – bdecaf Apr 12 '18 at 11:37