There are 2 US Post Offices in Stephens County serving a total of 9,250 residents equating to 4,625 residents per post office. It's estimated that approximately 14,764 packages are handled across the 2 county post offices annually. Stephens County is a county located in the U.S. state of Texas. As of the 2010 census, its population was 9,630. Its county seat is Breckenridge. The county was created in 1858 and organized in 1876. It was originally named Buchanan County, after U.S. President James Buchanan, but was renamed in 1861 for Alexander H. Stephens, the vice president of the Confederate States of America.