Why did the city of New Amsterdam become known as New York?

Dutch Governor Peter Stuyvesant surrenders New Amsterdam, the capital of New Netherland, to an English naval squadron under Colonel Richard Nicolls. Stuyvesant had hoped to resist the English, but he was an unpopular ruler, and his Dutch subjects refused to rally around him. Following its capture, New Amsterdam's name was changed to New York, in honor of the Duke of York, who organized the mission