Norge (pronounced Nor-gué) is what most Norwegians call their own country. Strangely, this name is less accurate than foreign appellations such as Norway in English or Norwegen in German. It is derived from the Old Norse Norvegr, which means exactly what the English and German terms still express - the way north. Norge does not signify anything to Norwegians except, of course, their country.
Unlike Sverige, Norge was not named by its own inhabitants. The country was established relatively late, about 1000 AD, and by that time international usage had already established the name of Norway for the whole area. In relation to themselves the Norwegians lived in the centre of the world, but to most others they were in the direction of north. In contrast to this there was also suthrvegar, the south way through Germany, and austrvegr, the east way of the Baltics.
Norge is also known as Noreg by some users of nynorsk, the rarer variety of written Norwegian. This is closer to the roots, but doesn't sound true to many Norwegians. Still, both varieties are allowed on stamps, bank notes and official documents.
Furthermore, I can pretty firmly state that Norge is not the origin of norgasms. Nor is it related to norg or nork, the Aussie term for breasts (so I'm told).