Sideshow Bob's Last Gleaming - S7-E9
Chief Wiggum: Hey, where is Sideshow Bob and that guy who, uh, eats people and takes their faces?
Guy Who Eats People and Takes Their Faces: I'm right here, Chief.
Chief WIggum: Oh. Then where's Sideshow Bob?
Prisoner: Eh, he ran off.
Chief Wiggum: Oh great! Well if anyone asks, uh, I beat him to death. Okay?
Officer Lou: Right.
Answer: Most of the races and cultures in Middle Earth do not use what we would call in a modern setting a "full name", that is a given name followed by a family name. The Hobbits are the only race that does this regularly (i.e. Frodo Baggins, Samwise Gamgee, etc). Most of the other races use the more medieval "son of" when stating a formal full name (i.e. Aragorn son of Arathorn, Gimli son of Gloin, etc). To answer the question directly, most of the characters that don't have last names don't have them because last names are not used in their culture.
BaconIsMyBFF