Until now, the rocket booster has been known as Big Falcon Rocket or BFR – although some believe the F in the name stood for something a little swearier!
The two-stage ship is designed to be fully reusable and will eventually replace the company’s Falcon 9, Falcon Heavy and Dragon rockets, the company says.
Musk revealed the name change for BFR on his Twitter account, before going into some extra details about the ship’s various names.
Starship refers to the crew-carrying upper stage of the ship, he said, adding that the rocket booster itself is called Super Heavy.
He also gave an insight into some of SpaceX’s plans for the distant future, responding to one commenter who suggested that the ship could not be called Starship unless it was sent on a mission to a different star system, by announcing “later versions will”.
Starship is still being developed, with TechCrunch reporting it could cost as much as five billion US dollars (£3.8 billion) to build.
The first private citizen to take a flight in the rocket will be Japanese billionaire Yusaku Maezawa, who has signed up to take a trip around the Moon – a roughly 240,000-mile journey which will take about a week and is scheduled to take place in 2023.