Funny thought - what if it's actually the United States, in Trek timeline, that broke up into a similar but different political entity?
Trek's WWWIII seemed to hit the USA particularly hard, if First Contact is anything to go by, with what appears to be a breakdown of the government as a whole. Also, just for fun, wasn't there some mention in a TNG writer's guide about native Americans being given back land and former nations by the 24th century?
It could be that many nations in Trek time still have their historical identities and even flags, but other nations have changed. Much as the Soviet Union no longer exists in our own time today, but we still think of many parts of eastern Europe with a "Soviet" tint, or flavor.