I discovered this very early case of a male name becoming a female name while reading about medieval English pet names that end with -ot and -et (e.g. Cissot for Cecilia, Ibbot for Isabella):
But the girl-name that made most mark was originally a boy’s name, Theobald. Tibbe was the nick form, and Tibbot the pet name. Very speedily it became the property of the female sex, such entries as Tibot Fitz-piers ending in favour of Tibota Foliot. After the year 1300 Tib, or Tibet, is invariably feminine.
Girl-cats were commonly named Tib during this period. (Boy-cats were called Gib.)
Tib reminds me of Toby, another male nickname used for girls. Toby, short for Tobias, was more popular as a girl name than as a boy name in the U.S. for most of the early 20th century (1910s-1940s).
Source: Bardsley, Charles Wareing Endell. Curiosities of Puritan Nomenclature. London: Chatto & Windus, 1897.