What was the name of the ship in the original "Alien"?

The ship in the original Alien is the Nostromo.

In Ridley Scott’s 1979 science-fiction horror film, the Nostromo is a commercial space tug carrying a massive mineral-refining payload back to Earth. Its seven-person crew is awakened from stasis after the ship’s computer, Mother, detects a mysterious transmission from a nearby world.

The crew lands to investigate and discovers a derelict alien spacecraft, where Kane encounters the eggs that begin the film’s nightmare. The Nostromo itself becomes the primary setting for the second half of the story, turning its industrial corridors, machinery, and ducts into a claustrophobic maze.

A common mix-up is the ship’s escape craft, which is called the Narcissus. The name Nostromo was borrowed from Joseph Conrad’s 1904 novel Nostromo, while Narcissus echoes another Conrad title. The film’s company is deliberately referred to mostly as “the company”; the Weyland-Yutani name became more prominent in later Alien stories.