How did The Beatles get their name?

The their early press interviews The Beatles were repeatedly asked about their name - particularly its unorthodox spelling. They gave many different and often contradictory explanations. This one, given by John Lennon, is particularly implausible.

Dusty Springfield: John, this is a question which you've probably been asked a thousand times before, but you always..., all of you give different versions, different answers, so you are going to tell me now. How did the Beatles get their name? 
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