Anzor is a given name. Notable people with the name include:
Anzor Astemirov (born 1976), Kabardian prince who heads the Yarmuk Jamaat, a chapter of the Caucasus Front
Anzor Chikhladze (born 1949), Russian professional football coach and a former player
Anzor Daurbekov (born 1977), Russian professional football player
Anzor Kavazashvili (born 1940), Soviet former football goalkeeper of Georgian ethnicity
Anzor Kiknadze (1934–1977), Georgian judoka who competed for the Soviet Union in the 1964 Summer Olympics
Anzor Kunizhev (born 1975), Russian professional football player
Anzor Sanaya (born 1989), Russian professional football player