The first correct answer to the Tennessee Trivia question came quickly from Jeff.
Question: Which is the only county in Tennessee named for a woman?
Answer: Grainger County
The Tennessee Blue Book notes that Grainger County (in East Tennessee) is named for Mary Grainger.
She was the daughter of Kaleb Grainger who came to TN from North Carolina. She married William Blount who was the first governor of the Territory South of the River Ohio (later Tennessee).