This was originally a male given name, then a surname. The Breton source, Iodoc, was translated into Latin as Jodocus. The Norman French transformed it into Josce, and when they invaded Britain, it made its first showing among English-speaking people in the form of Josse.
The name has had periods of popularity as both a boy's name and a girl's name. Some authorities believe it owes its current popularity among girls to its similarity to the happiest of girls' names -- Joy.