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The -th- sound is pretty rare among languages, and children often have difficulty learning to say it. So, a tiny child would easily do what comic foreigners (think Inspector Cluseau, whom I can't seem to spell but you know who I mean) do as well - pick a close-enough sound. So, the comes out de or ze, and Cynthy comes out Cindy.
It may also have been used as a pet form of Lucinda.