Grover \g-ro-ver\ as a boy's name is pronounced GROVE-er. It is of Old English origin, and the meaning of Grover is "grove of trees". Place name. Made popular in America by President Grover Cleveland. Also the name of a cute, furry, lovable little monster in "Sesame Street".
A baby name that sounds like Grover is Carver. Other similar baby names are Glover, Graves, Greger, Greer, Rover, Traver and Trever.