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First recorded in 1911, and possibly derived from Maggie, Margie or Mog, all short forms of the name Margaret.
From the 1800’s used to describe an ungainly lumbering Cow (or in the growing cities of the Industrial Revolution,  a “hag” or “lady of the night”). In parts of Lancashire, England the word ‘moggy’ means Mouse not a Cat at all.

Link: Origin of The Word Moggy