The entrepreneur would not reveal why he had renamed the craft, which has not yet been built, but added its rocket booster will be called Super Heavy.
In September, Mr Musk’s SpaceX company announced that Japanese billionaire Yusaku Maezawa had signed up to be the first passenger to travel on the ship.
The mission is planned for 2023 if the spaceship is built by that time.
It is the craft’s fourth name – it started out as Mars Colonial Transporter (MCT) and then became Interplanetary Transport System (ITS) before becoming BFR.
Over the weekend, Mr Musk tweeted that the spaceship was being redesigned, saying the new version was “very exciting. Delightfully counter-intuitive”.
Starship is due to replace the Falcon 9 and Falcon Heavy vehicles eventually and will cost an estimated $5bn (£3.9bn) to build.
Mr Musk’s plan is for Starship to take people into space on commercial flights around the Moon and Mr Maezawa would be his first “moon tourist”.
However, he will not land on the Moon but will travel on what is called a “free return trajectory”, which will bring Starship back to Earth after it has gone around the far side of the Moon.
Only 24 humans have visited the Moon – all of them Americans; 12 of them landed on the moon. Nasa’s Apollo 17 in December 1972 marked the last time humans landed on the Moon or went beyond low-Earth orbit.
Mr Musk’s longer-term plans are to take people to Mars and colonise the planet.
He did not reveal any details of the new design for the craft but had previously said it would be able to transport up to 100 passengers to Mars.
Mr Musk has had a troubled year.
In September, he was ordered to step down as chairman of electric car maker Tesla and pay a $20m fine, in a deal struck with US regulators over tweets he posted about taking the firm private.
He also found himself in another controversy after appearing on a podcast while smoking marijuana. Although the drug is legal in California, where the podcast was recorded, shares in Tesla fell more than 9% after his appearance.