Just as Bernstein with Maria, Bizet and Carmen also set in stone an extremely common Spanish name as being mysterious and exotic (another variant of Maria, as a 'Carmen' will always be 'María del Carmen').
I think it makes the name feel very different - mostly positive, but also in an exoticising/fetishising way - to those from outside the language culture, who simply don't realise just how many women and girls have those names. They are not a mythological or cultural equivalent of 'Cleopatra' or 'Cinderella'.