Also Queens, Manhattan, Brooklyn etc.
Where’d they get their names from?
Well, “Queens” is short for “Queens County”. I think the names Bronx and Brooklyn are derived from the Dutch, who were the original European settlers of New York. And my WAG is that Manhattan is derived from a Native American name for that island.
I don’t know why Staten Island is called Richmond.
IIRC, “Manhattan” derives from the name of a resident tribe. I could have sworn that the county name of Queens was King’s County, but I could be wrong.
You’re wrong. 
The borough and county names are as follows:
Manhattan - New York
Queens - Queens
Brooklyn - Kings
The Bronx - Bronx
Staten Island - Richmond
gila, you are wrong about Queens being part of King’s county. King’s County is the Borough of Brooklyn.
When Henry Hudson sailed the Narrows, he named the land to his left (facing north) after the States General of Holland, Staaten Eylandt.
Source: Staten Island Live.
The name Bronx is derived from Bronck’s Estate and the Bronck in question was a Swedish settler called Jonas Jonasson Bronck. Read more about it here
Or read all about it in the link already provided by peepthis…
Even after seeing this on their website, I think it’s a load of crap. (Nothing personal, capacitor.)
I live in a seaside community settled just after the turn of the last century. A popular story down here is how P.T. Barnum’s elephants were enlisted to help build the boardwalk. That story continues to be reported, based on a few photos of elephants holding timbers with their trunks. (They were PR photos).
I’ve also heard the borough got its name from a crewman on Hudson’s ship, asking about the landmass to his left,
“Is dat an island?” (Is Staten Island)
I have a copy of a Dutch seventeenth century map of Manatus, Gelegen op de Noot Rivier (“Manhattan on the North River”). Jonas Bronck’s estate is clearly marked on it.
What amazes me are place names live “Flatbush”, which supposed derives from 't Vlack Bos, meaning “a wooded plain”. Of course, I have this from Edward Robb Ellis’ book The Epic of Manhattan, and Ellis believed the story about the Sawing-Off of Manhattan, which Snopes has declared a real hoax (meaning that not only was the story of the sawing a hoax, but the hoax itself never actually took place. No contemporary sources refer to it.).