Josephina is fine, but I prefer
Josephine.
Josie isn't a bad nn, but I'd go with
Jo if it were me.
My son,
Josiah, sometimes calls himself
Josie, but he usually prefers Jak or
Jackson (Jak is his initials).
Josie is also a woman in the Netflix Daredevil (and the comics, actually) who runs a bar. She's at least in her 40s and grumpy, and since watching the show she's the first person I think of when I see the name
Josie. It's not an entirely negative association, but it is hard for me to imagine a
Josie who's a young girl.