Source: Bureau of Census
There's a story behind the name and the timing of the creation of each county that is now part of Virginia. For example, did you know we have a county named for the leader of the Yankee military that invaded Virginia in 1861 - but we have "lost" all the Virginia counties named for Thomas Jefferson and George Mason?
Carroll - Charles Carroll was a signer of the Declaration of Independence - but from North Carolina. In Southwest Virginia, anyone going downhill is going to follow the drainages into North Carolina or Tennessee. Because of the physical geography being an FFV from Tidewater meant relatively little to those folks in the Southwest... until the Virginia and Tennessee Railroad came through in the 1850's.
Grayson - William Grayson was one of the first two Senators from Virginia, elected to the First Congress. He was a strong anti-Federalist, and had opposed ratification of the Constitution. Supporters of the new Federal system (such as George Washington) were able to get Virginia to join the new union only after a close vote in a special convention, while Patrick Henry and others who opposed ratification were able to control the election of Senators by the General Assembly. Patrick Henry almost managed to get James Madison defeated in that first election for the House of Representatives, by getting James Monroe to run against him.
Amherst - Lord Amherst was the English general who gets credit for conquering Canada during the French and Indian War. That's the war George Washington helped to start in 1754, by "assassinating" a French diplomat as he slept in a camp in the Pennsylvania woods. Amherst was officially Governor of Virginia, but never actually set foot in the colony. [Amherst also gets credit for proposing germ warfare, sending blankets infected with smallpox to the Native Americans who supported the French. Hope they use lots of bleach when doing laundry in Amherst dorm.]
Franklin - Ben. You know about Ben... Note that Franklin City is nowhere near Franklin County, but they were both named for ol' Ben.
Hanover - When the son of Queen Anne died in the early 1700's, it was the end of that branch of the royal family. For a new king, when Anne herself died in 1714, Parliament chose a relative who was ruling a small territory in Germany, including the "Electorate" of Hanover. George I was the first English ruler from the House of Hanover - and we all know George III was the ruler during the American Revolution. (The royal family renamed themselves the "House of Windsor" during World War I, to obscure the connection with Germany.) The county was created in 1720, when George I was the king and it was politically correct to honor him.
Brunswick - this county was also formed in 1720. It also honors George I, referring to another section of the old home country in Germany. (Hey, so what if the new King of England never learned to speak English... the Virginia colony still knew how to appeal to the ego of people in power.)
Dickenson - the last county to be created in the state (the youngest, "Virginia's Baby") was named for Wiliam J. Dickinson. He was representing the area in the General Assembly when the boundaries for a new unit of local government were carved out of adjacent counties. Hmmm... guess there was no longer any reason to name a place after a member of English royalty in 1880, eh?