Cleeve \c-lee-ve\ as a boy's name is a variant of Cleavant (Old English), and the meaning of Cleeve is "cliff". The baby name Cleeve sounds like Cleve, Clive and Clyve. Other similar baby names are Clete, Clare, Claire, Clayre, Claude, Clause, Claes, Cleary, Cleavon, Clemmy, Clemmie, Clem, Cleon, Cleo, Clevon, Clyffe, Cliffe, Cloyce, Clyde, Colbee, Keefe and Olave.