So… yeah. Maybe the symbolism of this one isn't so very hard to dig out. But still, the gravestone is a very important element in the whole let's-turn-Scrooge-back-into-a-human-being project.
However invested Scrooge eventually becomes in his own spiritual life, and however bad he feels about the kind of man he has allowed himself to become, nothing really gets through to him quite like the gravestone with his name on it that confirms that the terrible, unmourned death he has been observing with the Ghost of Christmas Yet to Come is in fact his own.
It's this final discovery that really makes him desperate to change—to "sponge away the writing on this stone" (4.164). In a pretty powerful scene, the unemotional, angry Scrooge that we've seen so far suddenly gives way to a guy who bursts into straight up pleading. He doesn't know whether the phantom actually has any powers to change stuff, but he can't help screaming, "hear me! I am not the man I was. I will not be the man I must have been but for this intercourse" (4.160).
Just imagine a really good actor sink his teeth into that one—a showstopper for sure.