Cave is both a surname and a given name. Notable people with the name include:
Surname: Cave (surname)
Given name: Cave Beck (1623–c.1706), English schoolmaster and clergyman, author of an early constructed language Cave Johnson (1793–1866), U.S. Congressman from Tennessee and United States Postmaster General Cave Underhill (1634 – c. 1710), English actor Cave Johnson Couts (1821-1874), American soldier
Fictional characters: Cave Carson, character in science fiction stories published by DC Comics Cave Johnson (Portal), character in Portal video games