Clay \c-lay\ as a boy's name is of Old English origin. Occupational or place name involving clay, short form of Clayton. Clay that occurs naturally in the earth was a valued natural resource in earlier times. Boxing champion Muhammad Ali was named Cassius Clay after a 19th-century abolitionist, American statesman Henry Clay. Clay has 1 variant form: Klay. For more information, see also the related name Clayborne. Baby names that sound like Clay are Cloy, Caley, Cal, Cleo, Coley and Cully. View a list of the 9 names that reference Clay.