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Mog is short for Moggy or Moggie. The name is Cockney slang for "cat" or, more precisely, "alley cat." It is a derivative of Maggie or Margaret. The reference to the human name has sketchy origins: but the gist is that it refers to promiscuity, which alley cats have a reputation for. In Great Britain, alley cats are often referred to as "moggies." The term does not carry negative connotations, but is an affectionate term for a cat of undetermined origin.