The United States of America is a description of several states that are politically united on a continent of America. Like N.A.T.O. that expanded a bit, the U.S.A. has gone a bit beyond its geographic locator; Hawaii isn’t in America. Turkey isn’t on the North Atlantic.
It is possible that one day additional states may join the union. Venezuela, Chile, Mexico and Peru are obvious candidates. Territories of the United States of America may petition congress to be admitted as states, yet presently sovereign, foreign states in the Americas probably would be allowed to join the union if they were to accept the constitution of the United States and petition the congress for admission.
The Union of American States and Islands has a certain panache about it that may be lacking in The United States of America. With sufficient skill, reasoning and oratorical ability a President might get the designator for the United States of America upgraded to something else.