Mine is named Helios. Because of his nature, something that has to do with fire or the sun would fit best. I'm going to throw how about sol or solarus?
Epic luck charm by the amazingly talented Vephriel
I absolutely adore mine; he's my favorite pet (along with Banshee the undead wolf). I named him Aker. In Egyptian mythology they believed that the sun traveled through a tunnel to the spirit realm from sunrise to sunset. At either end of that tunnel was a lion guardian called Aker. The Aker eventually became Sphinx. I thought it fit since his body looks like the rays of the sun shining on him. I call him Tron cat though when I'm running with him ;p