This is more of a help. If the colonialist had won the revolution with Great Britain, could they have chosen a different names? Does the Republic of New Albion work?
Colombus discovers it
Colonia (Spanish last name of Colombus was Colon)
If it is discovered by someone and they take it as a new land to the west then these ones below.
Derivative of West in language of discovers (ex: Westeros)
Westerland (with natives being called Westerlings)
Ther problem is that they, and everyone else in Europe, called them "Americans" since that's the name for the new world that stuck.
I personally like "Novomundia" if you want an alternate name. It's Latin so it has that classical flair favored by enlightenment revolutionaries. It was the name Vespucci himself supposedly favored. It signals a radical break from the British past (which the USA liked to fancy itself). And it is not named after a person from Europe.
Problem is, how are you going to get millions of people who thought they were "Americans" to adopt a new name?