Q:

Why are The Hunger Games called The Hunger Games?

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.

A:

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 responsibilities 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.

A:

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:

Favored districts are better fed than less favored districts
Starving districts must resort to tesserae to feed themselves, which directly ties their submission to the Games
The tribute (and, IIRC, the District) that wins the Games gets increased rations 

