John Lennon: I just thought of it.
DS: You just thought of it...? Another brilliant Beatle!
John: No, no, really.
DS: Were they called anything else before?
John: Called, the uh, Quarry Men.
Ready, Steady Go, October 4 1963
'I just thought of it' was in fact another of the 'different answers' Dusty Springfield alludes to. The dispute as to how The Beatles go their name has never been definitively resolved.
We know that John called his original group The Quarry Men after the school all the members attended. When this connection expired there were experiments with a number of names, including the unlikely Johnny and the Moondogs. But a settled moniker was never established
By 1960 the name problem was becoming more pressing. According to John Lennon's first wife, Cynthia, there was then a drunken 'brainstorming session' in a Liverpoool pub at which Stuart Sutcliffe as came up with the name as a jokey tribute to to Buddy Holly and the Crickets. John then suggested reversing the French term les beat to create Beatles rather than the orthodox beetle. But this must have happened over a few months as there were further experimental versions of the name (Beatals, the Silver Beetles, the Silver Beats, and the Silver Beatles before the final one.
The Beatles publicist, Derek Taylor, offers an alternative naming myth. He claims that the Marlon Brando film 'The Wild One' (1953) directly inspired the name.
Taylor points to the scene in which Marlon Brando talks to his gang of 'young beetles' and it certainly true that the Brando look (leather jacket, cap, scowl) is the image The Beatles projected around this time.
The problem with this theory is that the The Wild One was banned in the Britain until 1967. Lennon was aware of the film but he could could not have seen it.
Or perhaps he travelled into the future and watched it on Youtube?