Final answer:
Charles II granted the territory of New Amsterdam, which became New York and New Jersey, to his brother, the Duke of York in 1664. The territory was named New Jersey in honor of Sir George Carteret's defense of Jersey Island. The name New York was to honor the Duke after the land was taken from the Dutch.
Step-by-step explanation:
In 1664, Charles II, King of England, regarded the territory of New Amsterdam as British by virtue of discovery and granted the land to his brother, the Duke of York, who eventually became King James II. The territory, which included present-day New Jersey, was part of the former Dutch colony of New Netherland. Following English acquisition, the Duke of York ceded a portion of the territory south of Manhattan Island, spanning from the Atlantic coast to the Delaware River, to Sir George Carteret and Lord John Berkeley.
To honor Carteret, who had defended Jersey during the English Civil War, this new proprietary colony was named New Jersey. The grant allowed Carteret and Berkeley to profit from the land but initially did not include governance rights, although they ultimately claimed these rights as well. New Amsterdam itself was renamed New York, not only reflecting the Duke's title but also his ambitions in establishing British North America's strategic settlements.