Respuesta :
Here is your answer:
According to my research when Stuyvesant surrenders New Amsterdam they decided to name New Amsterdam into New York in honor of the Duke of York, who basically made the mission. So, the answer would have to be option D "When the English captured the territory from the Dutch the king gave it to his brother, the Duke of York." Since how it was still named in honor of Duke of York.
Hope this helps!
~Nonportrit
D. When the English captured the territory from the Dutch the king gave it to his brother, the Duke of York