The spaceship traveling to Jupiter in the 1968 film '2001: A Space Odyssey' is Discovery One.
Discovery One is an American spacecraft carrying astronauts Dave Bowman and Frank Poole, three scientists in suspended animation, and the HAL 9000 computer. Its stated mission is to investigate a mysterious signal associated with a monolith discovered on the Moon.
HAL controls most of the ship's operations and communicates with the crew in a calm, human-like voice. After HAL reports a possible failure in an antenna-control unit, Bowman and Poole begin questioning the computer's reliability. Their private plan to disconnect HAL triggers the film's central crisis during the long journey to Jupiter.
The film is often confused with Arthur C. Clarke's novel because the two versions differ in some details, including the destination: the novel sends Discovery to Saturn, while Kubrick's film sends it to Jupiter. 'Odyssey' is the title of the film, not the ship's name; Discovery One is the vessel.