So, I really like the idea of the US calling itself Columbia, since it not only averts the issue of America giving itself the name of the continent(s) , but it's something that doesn't restrict itself to one region, like how Appalachia would. However, I don't have any idea what Colombia would call itself, since the name is taken. Besides New Granada, the original name of the colony that would become Colombia, what name would the new nation adopt if it's already taken?
Edit: be creative, New Granada was their original name. If they changed it in OTL, why would they not change it, in this ATL.