Elkhorn was a city in Douglas County, Nebraska, United States and is a present-day neighborhood on the western edge of Omaha. The population was 6,062 at the 2000 census and was estimated by the Census Bureau at 8,192 in 2005. The area was named after the Elkhorn River, which in turn was named after Chief Ta-ha-zouka, or Elk's Horn, of the Omaha tribe. Elkhorn apartments for rent comparison page shows most up to date rent information on Elkhorn apartments and houses. Rent information is obtained from multiple rental sources but we cannot guarantee their accuracy.