What is the name of the of the jail that Charlotte Doyle was in?
The name of the jail that Charlotte Doyle is consigned to on the Seahawk is the brig. A brig is a prison on board a ship or any military naval ship.
When Mr. Hollybrass is found face down with a knife stuck to his back, Charlotte is framed for the murder. Apparently, the dirk used as the murder weapon is the same knife Zachariah gave to Charlotte. Additionally, the dead man is clutching Charlotte's handkerchief in one hand; the implication is that Charlotte is the murderer. The sly Captain Jaggery has Barlow take Charlotte to the brig.
The brig is located in the hold, at the bottom of the ship. The hold is a 'tunneled dwelling faced with great wood timbers and rough planking grown corrupt with green slime. Charlotte discovers that this area is cramped with barrels and cases; moreover, the blackened bilge water lends a loathsome stench to the air.
To Charlotte's dismay, the brig is not a room, but a 'cage of iron bars with a gate for a door.' Barlow leaves her in the dark, and no one is more surprised than Charlotte when she discovers that Zachariah (presumed dead) is also in the brig with her.