When were these boroughs so named and after what or who(m)*: Manhattan, The Bronx, Queens, Brooklyn, Staten Island?

*m is for mainly pedants

I won’t do you the discourtesy of parroting from Wikipedia, Eliza. I know others here have excellent and more trustworthy toponomic resources and I’m sure that’s what you’re after. As you know, the members here are like buses, there’ll be another along in a minute. :)

The New-York Historical Society has a short answer.

Queen Braganza? Really? The New York Historical Society should gently take the lady to one side and correct her. She’s referring of course to Catherine of Braganza, who was the wife of Charles II. She would be styled Queen Catherine.

Michal, of royal blood, the crown did wear,
A soil ungrateful to the tiller’s care.
Not so the rest for several mothers bore
To Godlike David several sons before.

Dryden, as ever, encapsulates it perfectly. Poor old Catherine was barren and had to put up with her husband rogering and impregnating mistress after mistress and creating dukedom after dukedom to cater for his illegitimate sons.

Their account is basically right, but I’ve got some quibbles with it.

Manhattan: I have no clue who Robert Guet is, and the 1609 date is questionable. I presume he was a member of Henry Hudson’s crew, as that was the year that Hudson found the island and the river that bears his name. The OED dates the name Manhattan from 1625 in Dutch, citing J. De Laet’s Nieuwe Wereldt. English usage is in place by 1659. The word is from the presumed Munsee word *mənaháhte:nk, “where one gathers bows.”

Bronx: I have a date of 1641 for Jonas Bronck settling in the region. Bronck’s farm was called Broncksland, but the name died out, surviving only in the name of the Bronx River; and it is for the river which the borough was subsequently name.