Clayburn \c-laybu-rn, cla(y)-burn\ as a boy's name is a variant of Clayborne (Old English) and Clayton (Old English), and the meaning of Clayburn is "brook near a clay-bed; border near a clay-bed; clay settlement".
The baby name Clayburn sounds like Claybourn and Clayborn. Other similar baby names are Claybourne, Claibourn and Claiborn.