Camp Benning- later Fort Benning- was named in honor of Confederate brigadier general Henry L. Benning. Benning, who fought with General Robert E. Lee, earned the nickname "Old Rock" because of his coolness in battle.
I had already answered that I knew it from the top of my head and it must be Ft. Thomas, Kentucky, named after George Henry Thomas, the "Rock of Chickamauga" ... when I noticed ... George Henry Thomas was a Union general and born in Virginia ...
So I had to rely on Google once more ...
And here comes the correct answer: