Eagle Point is a city in Jackson County, Oregon, United States. The population was 8,469 at the 2010 census, up from 4,798 at the 2000 …Eagle Point is a city in Jackson County, Oregon, United States. The population was 8,469 at the 2010 census, up from 4,798 at the 2000 census. As of 2018, the estimated population was 9,408. In the mid-19th century, a rocky cliff near the location of what later became Eagle Point was a favored nesting place for eagles. An area resident, John Mathews, is said to have suggested "Eagle Point" as the name for a proposed post office in the community. The post office was established in 1872; Andrew McNeil was the first postmaster.