Was there any alternate names suggested at or around the time of the Declaration of Independence? IMO its probably the most annoying nation name in the world, as it uses the name for the continent,
That's only true if you consider all of the Americas to be one continent, which is illogical, if you don't do the same for Europe/Asia/Africa. In the U.S. we treat North America and South America as separate continents.
Anyway, I can think of plenty of other "annoying" names:
-Republic of China vs. People's Republic of China
-Republic of the Congo vs. Democratic Republic of the Congo
-Republic of Guinea (Conakry) vs. Republic of Guinea (Bissau) vs. Republic of Equatorial Guinea
-Republic of Korea vs. Democratic Peoples' Republic of Korea
-Dominican Republic vs. Dominica (Inhabitants of these two are called Dominicans and Dominicans, respectively.)
-United Kingdom (do no other united kingdoms exist?)
-Macedonia (which is forced to call itself "Former Yugoslav Republic of Macedonia" because Greece doesn't like the name)
-South Africa (which does not cover all of southern Africa)
Is "United States of America" really worse than all these?