In Assassin's Creed IV: Black Flag, Edward Kenway's ship is called the Jackdaw.
The Jackdaw is a brig that Edward acquires early in the story and progressively upgrades during his career as a pirate and privateer. Ship management, naval exploration and sea combat form a much larger part of Black Flag than in earlier mainline entries. The vessel serves as Edward's mobile base while he travels around the Caribbean.
The ship's name is often confused with vessels from other Assassin's Creed games. The Aquila belongs to Assassin's Creed III, while the Morrigan is associated with Assassin's Creed Rogue and the Adrestia with Assassin's Creed Odyssey. The Jackdaw is specifically tied to Edward's Caribbean campaign and remains central to the game's pirate identity.