AHC: A Jumble of News

The Age of Exploration brought a host of new placenames of the form New Oldplace. (or Nova, Nuevo, etc.)

Your challenge? Have three or more such places get the same names as in OTL, only in a different order.
For example, could New England have been named New Zealand, New France named New England, and New Zealand named New France?
 
Well, New York could have been called New Amsterdam if the Dutch had held onto it.

And Guyana's New Amsterdam, with a little bit of strech, could have been renamed New York considering the region was a British colony.
 
Well, New York could have been called New Amsterdam if the Dutch had held onto it.

And Guyana's New Amsterdam, with a little bit of strech, could have been renamed New York considering the region was a British colony.
That's the idea. Now do it with three or more.
 
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