When the Quarry Men were struggling on their way to becoming the Beatles in late 1959, they very briefly changed their name to Johnny & the Moondogs, Johnny being their leader, guitarist John Lennon. Johnny & the Moondogs was probably never considered seriously as a permanent name. The only known occasions on which the musicians -- John Lennon, Paul McCartney, and George Harrison, future Beatles all -used it was for a couple of occasions in the fall of 1959, in which they competed in Carroll Levis' "TV Star Search" contests.
By the beginning of 1960, they were back to using the Quarry Men, and in a few months, they renamed themselves the Beatals, switching to the Silver Beetles to the Silver Beatles and then finally to the Beatles by August 1960. Although there are some bootlegs credited to Johnny & the Moondogs, these are in fact rare Beatles tracks, billed to Johnny & the Moondogs as an in-joke.