Final answer:
The city of New York was renamed from New Amsterdam after the English captured it from the Dutch in 1664, honoring the Duke of York.
Step-by-step explanation:
The city now known as New York was originally called New Amsterdam. This name change occurred because the English captured the city from the Dutch in 1664. The Duke of York, for whom the city is named, was the brother of King Charles II of England. After the capture, the English renamed the city to honor the Duke. Therefore, the correct answer to the question is: a. Residents of the city voted to rename it in honor of the Duke of York.