So, I'm presently working on another new world mod of mine. Right now, I'm working on the colonial revolter system. Fundamentally, each culture group (that's actually likely to colonize the new world) will have one (or more) colonial revolters and associated colonial culture, and events to cause the change.
For the historical colonizers, this is not particularly difficult. For culture groups that have legends/oral tradition of long-lost lands that have, at one point or another, been associated with the New World, this is not especially hard either (Vinland for the Scandinavians, Fusang for the East Asians).
For the others, if one want to avoid pointless repetition of "New X", it gets significantly more difficult. Hence why I'm looking for ideas, and turning toward this forum for help.
French/Iberian/British groups: their historical colonies, which were both plentiful and lasting. No problem with those.
Dutch/Flemish: New Netherland
Russia (and perhaps all eastern slavs) will likely use Alaska/Alaskan (even thought that was only the name of one region of Russian America), because Russian America sounds awful.
East Asian cultures: Fusang
Scandinavian cultures: Vinland (Sweden probably get New Sweden)
The highest priority for ideas at this point would be the Germanic, Gaelic and Latin culture groups.
West Slavic, Turko-Semitic, South Slavic and Basque would come next.