Pick a country that is somewhat reminescent of your new civilisation. Find it's national language, and find out the word for "People", "Country", "Kingdom", or a landmark, like "River", "Mountain" or a deity's name, or something like that, then mash them together and modify the word a bit.
For example, if you had a civilisation that was historically barbaric, later becoming a series of kingdoms unified under a loose confederation in to a sort of an empire, with a penchant for theology and warfare, then take Germany as a rough analogue. Then, we have the German language.
Take "Forest Folk", or example, and translate it, and you get "Waldvolk", if I'm not mistaken. Now, modify it as much as you like. You might get "Valdoksland" or something. Land of the Valdoks, who came from the old region Valdok, which in proto-Valdokian was once "Waldvolk", 'people of the forest'.
Of you could take "Green Mountain". Translate to "Gruenberg". Now modify it. Say you get "Grenbarrg" or something. The people would be Grenbarrgs or Grenbarrgers. Now they travelled across the sea and settled an area of a new land and set up a kingdom, and called it Grenberrgia. This kingdom then dominated the whole region, and established a modern country, which is now called Granberland, as the language has evolved in time.
This is just an idea.
