In greek it does... well yeah because it is a noun and we have different suffixes for males-females-neutrals... Oh long story.
Anyway, it would (and it does) make more sense if all the Alexandra girls had "Alexander" as their surname, just like your girlfriend. In Greece we have different suffixes for male and female surnames, though if we use the surname in English sometimes it changes and gets the male suffix. I think that happens to nouns (surnames in this case) that end with the suffix -ος like Αλέξανδρος.