What is the name of Morpheus's ship in The Matrix?

Morpheus’s ship in The Matrix is called the Nebuchadnezzar.

The Nebuchadnezzar is a hovercraft operated by Morpheus and his crew in the devastated real world. It travels through the underground ruins left after humanity’s war with intelligent machines, while its crew enters the Matrix using neural-interface equipment.

The ship’s name refers to Nebuchadnezzar II, the ancient Babylonian king traditionally associated with the biblical Book of Daniel. That reference fits the film’s recurring interest in prophecy, dreams, kingship and religious symbolism. Morpheus himself is named after the Greek god associated with dreams.

Zion is not a ship: it is the last major human city. The Hammer is another human hovercraft, while the Logos is the vessel commanded by Niobe. The Nebuchadnezzar is especially important because its crew finds Neo, frees him from the Matrix and supports Morpheus’s search for the One.