The playable ship in Assassin's Creed IV: Black Flag is called the Jackdaw.
Edward Kenway captures and takes command of the brig at the beginning of the game. The Jackdaw becomes his base of operations as he sails through the Caribbean during the Golden Age of Piracy. Players can improve its hull, cannons, armor, storage, and other equipment.
The ship is more than transportation. Naval combat, boarding actions, hunting, exploration, and trade all connect to the Jackdaw. Its upgrades affect how effectively Edward can face forts and larger vessels.
The name is sometimes confused with ships from other Assassin's Creed games. The Morrigan belongs to Assassin's Creed Rogue, while the Adrestia is the ship used in Assassin's Creed Odyssey.