There are 3 US Post Offices in Hamilton County serving a total of 9,150 residents equating to 3,050 residents per post office. It's estimated that approximately 14,604 packages are handled across the 3 county post offices annually. Hamilton County is a county located on the Edwards Plateau in the U.S. state of Texas. As of the 2010 census, its population was 8,517. The county seat is Hamilton. The county was created in 1858. It is named for James Hamilton Jr., a former governor of South Carolina who gave financial aid to the Republic of Texas."