I have always wondered what would one call someone from Massachusetts had the colonies never managed to stay as one. I know it would probably still be a New English (New Englander whichever the term) federation. But if it weren't Bay Stater doesn't quit cut it. New Hampshire also poses a dilemma; the rest are easier.
Like most Latin-Americans I have always believed that the US monopoly on the term American is somewhat unfair. By now we can't help it so we learn to live with it. Unlike Canadians who suffer from an identity crisis every time one calls Canada part of America. We know better; America is a whole continent (or two depending how you look at it) and it just so happened to be that the founding fathers of the USA were not very creative. Which is strange since they could have gotten first dibs in the name Colombia/Columbia (both names much more poetic). Then Simon Bolivar and his guys would have either had to stick with Nueva Granada or call their union America.
I know Argentina was originally The United Provinces of South America and that the United States of Central America also existed both equally unoriginal. Thankfully the Argentines got creative. The Central Americans didn't but the tragic failure of their union resulted in the abandonment of such a boring name.
When the CSA was formed some thought definitely did go into the name. The term American was already established to refer to people from the US (definitively from inside the US maybe not so internationally). But the term Confederate allowed for some legroom to build a separate identity and denonym in case it was needed. In this way it is a much better thought out name.
For the alternate US name I am a fan of Appalachia even more than Allegheny/Alleghania (though the name becomes redundant once the nation expands). Virginia is also quite nice but New England would not like that and I am not so sure how the rest of the colonies would take it although in reality most of them were very much maintained by the Virginia Company (at least initially).
Also Argentina was an older term then you may think.
For an english equivalent of estadounidense, I think Statesider sounds ok.
I know Argentina was older and that is probably why The United Provinces of South America did not work. And as I said its a good thing it didn't. I personally do not have a problem with the US being called what it is. And in spanish the proper denonym is actually estadounidense, which unlike unitedstatian or usonian it does not sound stupid. Although we usually use gringo instead (which in not necessarily pejorative or rude).
For an english equivalent of estadounidense, I think Statesider sounds ok.