The Greatest Band of All Time went through quite a few names changes before settling on their famous (and, quite frankly, terribly punny) name. The Quarry Men, Johnny and Moondogs and then the Silver Beatles were all used before 1959.
They were big fans of Buddy Holly and the Crickets, and the the idea of Crickets had a nice double meaning but would be beyond American audiences.
They settled on the somewhat similar Beatles but often made up more amusing stories about its origins such a man on a flying carpet coming to their window and telling them the name. Nice.