The name remains on Virginia maps with the town of Fincastle, the county seat of Botetourt County. The town was evidently named after the English home of Governor Botetourt. Lord Botetourt was a very popular governor of the Virginia colony, and died just before the tensions of the impending American Revolution made the job much more difficult. John Murray, the Earl of Dunmore and Viscount of Fincastle, succeeded Lord Botetourt. Fincastle County may have been named in his honor, or for his son Lord Fincastle.
If so, the decision to change the name in 1776 is very logical. At that time, Lord Dunmore was leading the military opposition to the "rebels" in Virginia, and had already issued the infamous Emancipation Proclamation offering to free any slave who fled their Virginia masters and joined the royal British forces.