The name "Oakwood Cemetery" was chosen because of the large oak trees on the plot of 3 acres donated by B. S. Walcott for a public burial ground. It was doubtless called Walcott graveyard before it was named Oakwood.
The first grave of record is that of James G. Gilmer, who was born May 15, 1814, and who died April 5, 1846.
This will be an interesting find for you.