Glenice \g-leni-ce, gl(e)-nice\ as a girl's name is a variant of Glenys (Welsh), and the meaning of Glenice is "holy".

The baby name Glenice sounds like Glennice and Glynice. Other similar baby names are Glenine, Alanice, Glennie, Glenne, Glenene, Glenis, Glinyce and Lenice.