Of course you are perfectly right: a man is a man and a woman is a woman. But I'm sure you have noticed that I am not reasoning from a strictly etymological angle. I'm just trying to imagine what it is like to bear a name meaning "man" (if
Charles etc. does mean “man” at all) as a woman. So if someone called
Caroline believes, that her name means “woman” (or as you say “little woman”), I would say, this is a legitimate adaptation – even though of course strictly spoken it is not correct.
Andy ;—)