Cooray is a Sinhalese surname. Notable people with the surname include:
Anuradha Cooray (born 1978), Sri Lankan runnerAsantha Cooray, Sri Lankan academicCissy Cooray, Ceylonese social workerB. C. Cooray (born 1941), Sri Lankan cricket officialMervyn J Cooray , (Born 1938) Former State Minister of Power and Energy , Member of ParliamentSujith Cooray , Former Provincial Councillor of the Western Provincial Council , Member of parliamentReginald Cooray, Sri Lankan politicianThomas Cooray (1901–1988), 8th Archbishop of Colombo and first Sri Lankan cardinal