I don't recall any character from what is now the United States actually identifying as being from the United States. From individual states and cities, yes, but there's no evidence that the US still exists in Star Trek's 23rd or 24th centuries.
As for those states and cities, I don't see any particular reason to think the names would change in 300 years. They might, but I wouldn't take it as a given that they will. It's not really a very long time, in the grand scheme of things.