Your girlfriend has a great name. I like it.
I like
Clara but I don't like it much as a first name because I'm afraid people would shorten it to
Clare, which I don't like. Do you find that happens with your gf?
I think
Clara Josephine would be my first choice, but what about:
Clara SophiaClara LillianClara JaneClara MargotClara SusannahClara SylvieClara ThereseClara Theodora