The website Mental Floss has put together an exhaustive list of all of John Lennon's cats, from his childhood on through his career with the Beatles and up to his final days living in Manhattan with his wife, Yoko Ono. As it turns out, Lennon totally adored felines, and his distinctly acerbic wit came through in how he named them.
For example, Lennon's cat during the second half of the Beatles' career was named Jesus, which was likely a tongue-in-cheek response to the media controversy over his comment that the Beatles were "bigger than Jesus." (Paul McCartney apparently also owned a cat named Jesus, so this joke clearly went over well with the Beatles camp.) Later on, Lennon would have a pair of cats, one black and one white, that were named Salt and Pepper, and another pair of rescued strays named Major and Minor.
Lennon's first cat as a young boy was named Elvis Presley, which he and his mother named after the singer, though they would eventually discover that the cat was female when she had a litter of kittens in their cupboard.