Can you describe the cat? I'll list some names anyway without the pic and you can choose which one you like.
Actaeon (ak tee' on) - he was the guy that saw Artemis bathing so she changed him into a stag
Aea (ee a) - it was a city in Colchis, the place where Jason went to find the fleece
Argo - we all know what that was, and no I don't mean Xena's horse
Calydon (kal' i don) - he's not important, but I liked the name
Corinth - you could call him Cori for short
Deimos (die' mos) - it's pronounced die mos. I've been saying day mos. Oh well. He was god of fear, terror, and was a son of Ares. I just like that name cuz Joel Tobeck played him.

(PS. That goes for Strife, too ;))
Diomedes (die o mee' deez) - I just like the way it sounds
Elysiam (ee lee see um) - okay so I kinda made that one up. I'm sure I've heard it somewhere before, but I like it.
Endymion (en dim' i on) - I'm a Sailor Moon fan too
Eteocles (e tee' o kleez) - I just thought that one sounded cool
Hercules of course

and
Iolaus as well and can't forget
Jason
Ixion (ik' si on) - another one I thought sounded cool
I'm gonna stop now because there are just *so many*, but if you want more I'll continue. I have this book, Dictionary of Classical Mythology, and it has almost EVERYTHING. That's where all these names are coming from. But let me know if you want more.
Eurydice