The more likely origin is a Sabine name that was Romanized as "Clausus", a homophone (and possible cognate) of the Latin perfect passive participle of claudō, meaning "shut, closed". The idea that the name came from the word "claudus" may be a folk etymology inspired by the Emperor Claudius's own physical disabilities.
Can somebody please take the word "cripple" out of the meaning/description/history? I know it might "mean" that, but many people would be offended by that.