In Suzanne Collins' 'The Hunger Games', the nation is called Panem.
Panem is a fictional country formed from what remains of North America after an unspecified series of disasters and wars. Its name echoes the Latin phrase "panem et circenses," meaning "bread and circuses"—a reference to rulers pacifying the public with food, entertainment, and spectacle.
The nation is ruled from the Capitol, a wealthy and authoritarian city that controls 12 outlying districts. The districts produce resources for the Capitol, while the annual Hunger Games punish them for a past rebellion and reinforce the government's power. District 12, where Katniss Everdeen lives, is therefore a district within Panem, not the name of the nation.
A common mix-up is choosing North America, since Panem occupies its post-apocalyptic territory. North America is the former geographical region; Panem is the political entity in Collins' story.