Claver is a Spanish surname. Notable people with the surname include:
Francisco Claver (1926–2010), Filipino priest Isaac Claver (born 1989), Spanish politician Peter Claver (1581–1654), Spanish priest Víctor Claver (born 1988), Spanish basketball player
See also Mauricio Claver-Carone, American political advocate Claver, Surigao del Norte, a municipality in the Philippines