What countries have the word "America" in them? How many countries in the Americas are "united States"?
What do you call a citizen of the United Kingdom of Great Britain and Northern Ireland?

For the record, The United States of America is the only country with the word America in it's name. Our immediate neighbor, The United Mexican States, is another country you could, but no one would, plausibly call the United States.

The British isles contains two countries, Ireland and the UK. One of these is the home of the British, and the other would be much happier if you didn't call them that.

Insisting that you not refer to the people of a country by the most unique name in the countries name, because the geographic region has that word in common is ... Odd.