It depends on your family, I guess. In my family, a cousin isn't necessarily all that close--I see most of them at least twice a year, but I don't spend time with them outside family gatherings. So if I liked any of their names (and I don't, not enough to want to use), I wouldn't feel all that awkward about using them. Besides, none of them are bad people (well, none of them are
terrible), so I wouldn't mind if the fam thought I named the kid after them. ;) You might spend a lot of time with your cousins, though, or there might be a sort of unspoken rule about repeating names. I don't know; yours isn't a situation I can judge, especially not over the internet, with no idea of what your family's like.
I think
Julia is a lovely name. It used to be one of my favourites--and
Julia Prudence was my favourite combo/double name (I was attached to Julia-Prudence, too, you see). Others I've been fond of have included
Julia Snowdrop,
Julia Snowbird,
Julia Song, and
Julia Rae. You might like
Julia Margaret,
Julia Charlotte,
Julia Violet,
Julia Charis, or
Audrey Julia.
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