Allegany is a town in Cattaraugus County, New York, United States. The population was 8,004 at the 2010 census.The Town of Allegany is on the south border of the county, west of the City of Olean. There is a village named Allegany inside this town.The origin of the name Allegany is uncertain. It may have come from the name of a tribe called Allegewi that lived along the Allegheny River’s banks. It may also be based on an old Native American word meaning ‘lovely’ or ‘beautiful.