Could be Stone Mt.
There's a place near me called 40 acre rock. Basically, it's a giant rock, but it's actually about 14 acres. There are other large rock outcroppings that extend about 40 acres total.
Anyway, there's stuff like that all over it. Pretty cool.
It was sort of a tradition to mark your name and the date in it up until they started "protecting" it about 20 years ago.
As kids, we'd go there with the family for picnics, and for nature walks and things.
As teens, we'd go there after dark to camp out, bonfire, get drunk and otherwise inebriated in various ways, and to get laid. Of course and as a teen, you'd be head over heels , and you'd write both your names in the rock surrounded with the usual heart and arrow design with the words forever in there.
Most of the more recent names disappear after a while, getting worn away by the weather and foot traffic, since they really weren't that deeply inscribed.