Interestingly enough, the United States of America is the only country in the world with "America" in its name. Not that it's any justification--I believe the Greeks have a similar bone to pick with Macedonia.

None of the States used America, but just as separate countries created the Union, wait European Union the United States used of America to designate where they where. Now in 200 years people might still think of France and Germany as separate countries, but I don't think the distinction is going to last that long.

I'm not entirely sure of common usage, but my anecdotal experience is that people in Latin America refer to the people of the US as "North Americans," while in Spain I've heard what would translate as "United Statesian."