I know wikipedia isn't generally the most trusted source for this sort of thing, but: "[Claudia] comes from a Roman family name which was derived from Latin claudus meaning 'nice, kind-hearted'."
I always thought it was weird that a name taken by Roman emperors had such an unfortunate meaning, though a lot of Roman names weren't exactly of the flattering sort. Still, I don't think Claudia's meaning, whatever it is, makes it something that would be an infliction, considering the fact that probably less than 1% of non-namenerds have any idea what its meaning is.