Even though the US McFly claimed the name first there's no law that says either band has to give up their name.
But as the US band are planning to tour the UK soon McFly fans should watch out for confusion.
"It could be a bit of a pickle," US McFly exclusively told Newsround Showbiz.
McFly aren't the first band to come across the same name problem.
Liberty X started out life as Liberty, until a band with the same name took them to court.
And Blue also went to court after a 1970s band tried to sue them and their record label for up to £5m.