Good question. I always wondered about that too. Things I came up with were Columbia, Batavia, Nova Belgica/New Belgium. The last one because Belgica/Belgium was used as a synonym of the Netherlands.In a TL where the New Netherlands survives, then undergoes a successful war of independence, what would they change their name to?
Hudsonia, after the Hudson River? 'America' is named after an Italian, after all.