As a trading post
Holland
New Amsterdam.
The Dutch called this colony New Amsterdam.
The Dutch. The city was named after their own capital Amsterdam: New Amsterdam.
No state went to Amsterdam. The Pilgrims went to Amsterdam first and then return to England. In 1620 they established Plymouth colony. New Amsterdam became New York.
The answer is New York.
The Dutch in 1613 established a fur trading settlement in what is now lower Manhattan. It was called Nieu Amsterdam (New Amsterdam) starting in 1625.
New Amsterdam was a DUTCH colony. founded by Petert Stuyvesant. Subsequently it became New York.
There is some strange English in your question, but New York started out as New Amsterdam, a colony and trading post established by the Dutch.
It was already an existing Dutch colony named New Amsterdam and had considerable infrastructure in place so what better way than to simply switch names.
The capital of New Netherland colony was New Amsterdam, which is present-day New York City.
New Amsterdam