From the Latin female name, a feminine form of Claudius. The name is mentioned in one of St Paul's letters to Timothy (2, 4:21 ‘Eubulus greeteth thee, and Pudens, and Linus, and Claudia, and all the brethren’), as a result of which it was taken up in the 16th century and has since maintained a steady popularity.
English: habitational name from places in Buckinghamshire and Somerset. The former was earlier Rockholt, and was so named from Old English hrōc ‘rook’ (perhaps a byname) + holt ‘wood’. The second element of the Somerset place is probably (and more predictably) Old English well(a) ‘spring’, ‘stream’ (see Well).