I absolutely adore the name
Ximena. I pronounce the "x" as an "h," is that correct in Basque?
Zurine is interesting. They do like their "z" names, don't they?
Do you like
Edurne? I've got that on my long list and I'm pretty sure it's Basque. Others you might like (again, I'm pretty sure they're Basque too): Elixabeta,
Arantxa,
Calixta.