I'm just interested in how the New York name developed in terms of the city and the state.
Was there a city called New York that grew so large and wealthy that it was able to become one of the original 13 colonies?
Or was the colony created and a city named New York after that?
Also what factors went into deciding to name them the same thing? Was there a dispute over the name of either?
In 1664, English representatives from Connecticut forced New Netherland (Dutch colony) Director-General Peter Stuyvesant to recognize their control over English towns on Long Island. King Charles II of England granted his brother, James, Duke of York, claim to lands in North America around the Hudson and Delaware Rivers, even though the Dutch still claimed them. James was quite pompous and arrogant which is why he enjoyed the name New York, after his title as the Duke of York (he was also Duke of Albany, leading to the change of Beverwijk to present-day Albany). In the same year, the English would conquer New Amsterdam, and rename it New York City. There was no bloodshed, which many attribute to Richard Nicolls' (soldier and loyal friend of the Stuart cause) policy of accommodating many Dutch property claims. That is largely why many neighborhoods in New York still have Anglicized Dutch names (Harlem = Haarlem, Brooklyn = Breuckelen) The Dutch claimed the province again, in 1673, but the English forced them to return it via the Treaty of Westminster the following year. Eventually, James bought the whole of New Netherland from the Dutch in exchange for the Isle of Run in the East Indies.
Edit: Correction from West Indies to East Indies...Isle of Run
New York (state and city) was originally apart of the Dutch colonies of New Netherlands known. New York (city) specifically was originally New Amsterdam which was where Manhattan is today.
Both had their names changed to New York after they were given to the Duke of York by the English crown upon being obtained after the disastrous Anglo Dutch war where New Amsterdam was traded for the English East Indies colony of Run which effectively gave the Dutch a monopoly on several goods and dominance of the East Indies and the spice trade.
New Netherlands was formed around 11 years before the founding of New Amsterdam (1614 to 1625) which would eventually become New York City. Though other portions of New York City (such as Staten Island) were settled a bit before (in 1624).
Though, it should be mentioned New Netherlands included other lands outside of New York (state) such as New Jersey, Delaware, and Connecticut so whether you consider that to be the precursor of New York state is up to you. Otherwise, New Amsterdam (aka New York City) was formed first.
The Dutch Republic by Jonathan Israel.
In the year 1664 the English sent Colonel Richard Nicollis to seize New New Netherlands from the Dutch. The names were changed to make them more English. Please see Conceived in Liberty, Vol 1. Part IV, The Rise and Fall of New Netherlands for a deeper discussion concerning the back and forth of this area between the two countries. This book is freely available at the link below.