Old Grandad is an ancient and very, very, very large troll that appears only in The Light Fantastic. His nickname comes from his membership in the family of Kwartz, Krysoprase, Beryl, Jasper, and Breccia, and his real name is unknown.
He is large enough that his face is at first mistaken for a cliffside and his teeth are the size of tombstones. For quite some time, he had been peacefully philosophizing, and was nearing the point of troll death- after trolls philosophize for long enough in one place, they become rock and lose all sentience. Just before this point, he is awakened when the gang of bandits led by Herrena the Henna-Haired Harridan unknowingly lit a fire in his mouth, believing it to be an ordinary cave.
He'd just managed to stand up and begin to give chase when the sun rose and, presumably, put him back to sleep.
While it appears to be a nickname only, 'Old Grandad' is nonetheless the only name given to this troll, making him so far one of the only trolls in the Discworld series not to be named after a known rock or mineral.
However, there is obviously some influence from the Roundworld rock formation known as The Old Man of the Mountain, in New Hampshire.