Whatever name you choose will be a good name - you're the author! You probably want a short name that sounds primitive. I'd suggest browsing through the links in this related question to help you come up with some good choices.
Neanderthal?
Alley Oop , who was a time traveling caveman created by V.T. Hamlin in 1932 .
Stanley's nickname is caveman
caveman charlie i a person that loves you
Stanley is called "Caveman" in the book Holes because after he found a fossil of a fish all the boys from his tent all said he must be a Caveman being able to find that. Thats how he got his nickname :)
caveman in the movie holes is Stanley yelnats IV
because he lives in a cave
In the book "The Pact," Caveman's real name is James.
Go to this link --> good information there: http://en.wikipedia.org/wiki/Caveman
The song used in the Lynx Caveman advert is called "Cold Little Heart" by Michael Kiwanuka.
frogs get there name from the caveman
A hobo/caveman.
Neanderthals.
It is impossible to know his name
Alley Oop , who was a time traveling caveman created by V.T. Hamlin in 1932 .
Stanley's nickname is caveman
Daniel Caveman Diaz goes by Caveman, and Synyster Caveman.
Homer-Erection