The band Muse, who own the worldwide performing rights to the name, had threatened to sue.
Francine Chaloult, Dion's publicist, said the name "Celine Dion Muse" will now not be used, according to a report on the Jam!Showbiz website.
A spokesman for Muse's record label said they had offered to let Dion use the name - as long as it was not in the title or in connection with CD and video sales.
The Teignmouth band feared its use would affect their chances of cracking the US market when they tour there in 2003.
The band's lead singer, Matthew Bellamy, said: "We don't want to turn up there with people thinking we're Celine Dion's backing band."
Lawyers representing Dion told Billboard.com that "Muse" was only one title being considered for the show.
They said: "We were talking to them to try to work it out, but they made unrealistic demands to get the clearance."
A spokesman for Taste Media, the band's record label, said: "We said we were happy for Dion to go ahead and she could use the name, as long as it was not used in the title or in connection with any CD or video sales.
"But in a letter sent to us, the lawyers said: 'My client cannot accept the conditions. 
"Our client will proceed without the proposed settlement and use the marque "Celine Dion Muse" for its show and related goods and services'.
"We thought we own the name the name, why should we give up?
"They didn't tell us other names were being considered. They just came back with money."
The band rejected an offer from Dion's management company to buy the rights for $50,000(£32,000).
The news that Dion has decided to drop the name has been take stoically by the band.
Award winners
Taste Media's spokesman said: "From our point of view, the job's been done."
Dion will appear in Las Vegas in March, at a new 4,000-seat theatre at Caesar's Palace casino.
The concert is scheduled to run for a minimum of three years with tickets costing up to $1,000.
Muse have two albums, Showbiz and Origin of Symmetry, and sold three million records worldwide.
They have won the 2001 NME Best Band award, the 2002 Kerrang! Best Live Band award and are up for the of Best Live Band of 2002 in the Q Music Awards.
