Jenny

google

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early 17th century (used to denote a female mammal or bird): pet form of the given name Janet (compare with jack1).

wiktionary

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From the name Jenny, a diminutive of Janet.

etymonline

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Jenny

fem. personal name, originally another form of Jane, Janey and a diminutive of Jane or Janet; in modern use (mid-20c.) typically a shortening of Jennifer. Jenny is attested from c. 1600 as female equivalent of jack (n.), and like it applied to animals (especially of birds, of a heron, a jay, but especially Jenny wren, 1640s, in bird-fables the consort of Robin Redbreast). Also like jack used of machinery; Akrwright's spinning jenny (1783) is said to have been named for his wife, but is perhaps rather a corruption of gin (n.2) "engine."