Duncan is a town in Spartanburg County, South Carolina, United States. Its population was 3,181 at the 2010 census. In 1811, a post office was established on what is now S.C. Highway 290. A tiny settlement sprung up around it, and both the post office and community were named New Hope. In 1854, the town changed its name to Vernonville or Vernonsville in …Duncan is a town in Spartanburg County, South Carolina, United States. Its population was 3,181 at the 2010 census. In 1811, a post office was established on what is now S.C. Highway 290. A tiny settlement sprung up around it, and both the post office and community were named New Hope. In 1854, the town changed its name to Vernonville or Vernonsville in honor of local physician J.J. Vernon.