Jérôme

An older form of this name is Jéronyme (also often found written as Jéronime), which is obsolete in this day and age. It originates from the medieval period and was unisex at the time.

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In turn, it should be a variant of Hiéronyme (also often found written as Hiéronime), which is the French form that is closest to the original Greek name Ἱερώνυμος (Hieronymos). It was also unisex and is now also obsolete.

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With that said, it seems to me that Jérôme might initially have started out as a contracted (i.e. shortened) form of Jéronyme, which was a longer name and thus a bit more cumbersome to write and pronounce. For reasons unknown, this particular abbreviation appears to have been limited to male bearers and eventually became the dominant French masculine form of Ἱερώνυμος (Hieronymos).