The English were not the only group of Europeans interested in the Western Hemisphere. The French, Spanish, Portugese and Dutch all sent their own explorers to recce the area and most importantly of all see if they could make any money out of these new lands. In the case of New York, it was actually the Dutch who took the initiative in this area, although confusingly through the actions of an Englishman working for them; Henry Hudson. He was working for the The United New Netherland Company. The Dutch named these lands New Netherlands. The ownership of the lands would pass to the Dutch West Indies Company in 1621.
The Dutch and English were serious rivals throughout the Seventeenth Century and they would fight countless wars across the globe. Locally, more and more English settlers were pushing into the interior from the coastal New England states and so were coming up against Dutch company rule. It should be said that many Dutch settlers were uneasy at being ruled by a commercial company and resented many of the powers of their landlords.
The English run State governments were not at all happy at the legal and taxation loopholes that New Netherlands provided. For example, Virginia tobacco could be smuggled into New Amsterdam and then sent on to anywhere in the world and so avoid customs duties.
The English were moved to try and remove the Dutch from the middle of their Atlantic seaboard colonies. This course of action was to be enthusiastically endorsed by the English colonies themselves. So, in 1664, Charles II now, based on the claims of John Cabot in the fifteenth century, coolly gave the entire country, from the Connecticut to the Delaware, to his brother James, the Duke of York. This ignored the inconvenient fact of the Dutch colony's existence. Richard Nicolls of the Royal Navy set out with a small fleet and about five hundred of the king's veterans. Reaching New England, he was joined by several hundred of the militia of Connecticut and Long Island, and he sailed for the mouth of the Hudson and New Amsterdam.
Unfortunately for the Dutch company governor the timing could not have been worse. He was busy in the North of the territory quelling an Indian uprising. He had to race back down to New Amsterdam and try to rally the population for the defence of the colony. However, many of the inhabitants of New Amsterdam were now English and even the Dutch settlers would not be stirred by patriotism to defend the monopoly and powers of a commercial company. Reluctantly, the governor handed over the fort without bloodshed to the Duke of York. Hence the name New York was coined from 1664.
It should be said that the Dutch would get their revenge elsewhere on the English many times over in a series of wars over the next two decades. In fact they would reoccupy New York in 1673 but it was handed back to the English under the terms of the Treaty of Westminster in 1674.
New York was still to have painful growing pains as the existing Indians and the French coming down from their St Lawrence settlements would still cause no end of skirmishes and even all out wars for the interior. The French and their Indian allies would ultimately only cease to be rivals after the Seven Years War from 1756 to 1763 in which the French would lose virtually all of their Canadian and Great Lake settlements.