Carve Name into Stone

What I wanted to write was a story about carving a name into stone, hoping to be immortal, but it turned out to be immortal. But is this kind of immortality what people want? Civilization is ultimately short-lived on a cosmic scale. It is very likely that at the end of all technological culture, only a few names will be left around the home planet. But in the almost infinite time after that, will there be a few concerned spectators stopping here? What will they do with the information they took such pains to retain?