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From the Wikipedia article:
"After the signing of the Treaty of Westminster in November 1674, the city was relinquished to the English and the name reverted to "New York". Suriname became an official Dutch possession in return."
How I, and most people I know, learned it we traded New York for Surinam. From the quoted piece it turns out it was not really a straight trade, but part of a peace treaty.
It does make you wonder why 2 neighbors who have an argument fight it out on the other side of the world.