Cleevant \c-leeva-nt, cle(e)-vant\ as a boy's name is a variant of Cleavant (Old English), and the meaning of Cleevant is "cliff". The baby name Cleevant sounds like Cleevont, Cleavon and Clevon. Other similar baby names are Cleanto, Cleante, Clement, Cleveland, Cleavland and Levant.