Final answer:
New Amsterdam was the Dutch colony established on Manhattan Island, later seized by the English in 1664 and renamed New York after the Duke of York.
Step-by-step explanation:
New York was initially founded as a Dutch colony and was called New Amsterdam. It was established by the Dutch in 1624 on Manhattan Island and developed quickly as a bustling center of trade. During the Second Anglo-Dutch War, the colony of New Netherland, which included New Amsterdam, was seized by the English in 1664. Subsequently, the colony was renamed New York after the Duke of York, the brother of King James II of England. This renaming marked the English control over the area, which had previously been a point of competition between the Dutch and the English commercial interests.