Rush is a town in Monroe County, New York, United States. The population was 3,490 at the 2020 census. The town is a suburb of Rochester located in the southern part of the county. Rush was established in 1818 from the town of Avon in what was then Genesee County. It was either named after the rushes growing along the creek…Rush is a town in Monroe County, New York, United States. The population was 3,490 at the 2020 census. The town is a suburb of Rochester located in the southern part of the county. Rush was established in 1818 from the town of Avon in what was then Genesee County. It was either named after the rushes growing along the creek, or after Dr. Benjamin Rush, a Founding Father of the United States.