There are 4 US Post Offices in Rappahannock County serving a total of 8,224 residents equating to 2,056 residents per post office. It's estimated that approximately 13,126 packages are handled across the 4 county post offices annually. Rappahannock County is a county located in the Commonwealth of Virginia. As of the 2010 census, the population was 7,373. Its county seat is Washington. The name \"Rappahannock\" comes from the Algonquian word lappihanne (also noted as toppehannock), meaning \"river of quick, rising water\" or \"where the tide ebbs and flows.\" Rappahannock County is included in the Washington-Arlington-Alexandria, DC-VA-MD-WV Metropolitan Statistical Area."