Trump's definitely referring to the United States with his pointless renaming attempt because it's singular and not plural, but I'd be careful accusing him of thinking about anything. I doubt he does that very often.

I guess the Organization of American States exists. But usually it's pretty unambiguous which sense is being used; like, I guess you could call Mark Carney an American head of government but it's basically just being obtuse, unless it was in the context of, say, a meeting of Carney with other heads of government in the hemisphere, and then it'd be unambiguous what was meant.

Even "United States of America" is not unambiguous in the most pathological case; Mexico is also a country consisting of united states existing in the Americas.