The United States Of America is a title with little meaning and one that does not distinguish it from any other country in North, Central, or South America. All these countries are united states and they are all in the Americas.
Imagine if France changed its name to The United States Of Europe. Imagine then if they called themselves Europeans, as if other people in Europe aren't European. That's exactly what the US has done. It has hijacked the name of its continent from others that also occupy it.
In fact there's another country that gives itself the united states title, and it's right next to the US. Most call it Mexico, but it calls itself The United Mexican States. This name actually makes complete sense because it specifically describes that country and that country alone with the word Mexican. That word describes only people of that country, while the word American describes people from any of the Americas.
The term Yank, or Yankee, seems to be the best way to describe people from the US without referring to anyone else. Therefore, the new name should be The United Yankee States. Some might think this term is offensive, but that's subjective. I'm from the US and am not offended when I'm called a yank. In fact many of my family members that are not from the US affectionately call me yankee because I'm from here, so I kind of like it already, but maybe that's just me.
Just a thought...