Claybourne \c-laybour-ne, cla(y)-bou-rne\ as a boy's name is a variant of Claiborne (French, German, Old English) and Clayborne (Old English), and the meaning of Claybourne is "boundary with clover; boundary of clay; brook near a clay-bed; border near a clay-bed".
The baby name Claybourne sounds like Claybourn and Claibourne. Other similar baby names are Clayborn, Claibourn, Klaibourne and Clayburn.