Changing of name had a political meaning. Originally, what is now NY, was named New Angouleme and proclaimed property of French crown by explorer Giovanni da Verrazzano in 1524. In 1527 Spanish published a map were territory is named Land of Esteban Gómez after the first Spanish explorer to visit the area. Then Dutch came, they naturally slapped they own names- New Netherland for entire region and New Amsterdam to the colony. So, then (in 1664) British took over, it was only natural to rename it honor of one of the British royals. It was done to mark the territory, show supremacy.

None of such contest went over New Zealand. For British it was just a name used in old Dutch map. They anglicized it, at that stuck. No one contested islands, so British had no urge to make a demonstration of having control of them.