Lackjaw
Lackjaw was a dwarf jeweller working in a small, unnamed city relatively close to Ankh-Morpork during the events of The Light Fantastic.
As a Dwarf, when the Red Star appeared, he drew the ire of the Star People, who, in addition to their burning of books and killing of wizards, wanted to kill all the "magical" (i.e. non-human) races. Lackjaw helped Cohen the Barbarian twice- first, by making dentures for him out of troll teeth, and second, by helping him frighten off the Star People with his large and dirty axe (guaranteed to add tetanus to the terrors of warfare).
Lackjaw and Cohen then attempted to flee the city, but were cornered by the Star People just as the Luggage appeared. The two of them then rode the Luggage in pursuit of Twoflower, Rincewind, and Bethan- the Luggage, hellbent on finding its master, didn't seem to mind. What happened to the dwarf after that is unknown; he didn't accompany Cohen to the University. It is very possible that he has been absorbed into the great melting-pot that is Ankh-Morpork. The Compleat Ankh-Morpork lists a firm of "dental technicians" based on Whalebone Lane called Lackjaw and Armsgrafter. This firm manufactures dentures, bespoke or off the peg, and can replace single teeth in wood, bone, steel or "recycled". They also trade in troll diamond teeth, but whether they buy them or replace them is not known.
Annotation
The entry on Lackjaw and Armsgrafter in The Compleat Ankh-Morpork goes through the history of Roundworld dentistry in several words. False teeth were indeed once made of wood - there is a famous Monty Python sketch about this. Others preferred carving replacements out of animal bone, and some inventive dentists made their false teeth out of harvested human teeth (battlefields and corpses were a preferred route of supply - it wasn't just gold teeth that the Royal Sto Plains Riflers would harvest as plunder.). Some dentists, way ahead of their time, tried to regraft viable teeth into new jaws. As blood typing and basic asepsis were not known about, this could lead to agonising pain as rejection and necrosis set in. Steel teeth were tried in Soviet Russia. At least one James Bond villain touted them.