Wow, what a great link, badkittypriestess! Lots of great Greek gods & goddesses names there. There were also links to other cat name sites at the bottom of the page; I checked out the Celtic ones - some great and interesting ones there too.
Good luck with the new Mercotan kitty!
Too bad he’s male. I always figured that Penelope, (ripping apart the day’s weaving every night), was a good cat name.
(Basileus is king. Basilious sounds like Basil the bilious, to me. 
)
Pheidippides (if anyone can remember the spelling or pronunciation) was a runner–the guy who ran the first “Marathon,” (dying at the end of his run, but that was after having already run to Sparta and back (150 miles in two days) for help and then fighting in the battle, and only then running another 21+ miles from Marathon to Athens). (The legend, corrections, and alternative names can be found scattered around the internet.)
Deinosailuros would mean “terrifying cat.”
Shouldn’t that be “Mew-saka”?
d & r
The name comes in both spellings:
Basilius Valentinus
Basileus
Damn, there goes my two. How about myoclonic dystonia, Toni for short?
Vlad/Igor
If the cat is a gift, how about Doron?
That’s a satisfying name to call a cat when it runs into a mirror or falls into the toilet, anyway.
I like the name Phaedra, m’self. And then she gets an extra-cool Nancy Sinatra/Lee Hazelwood duet that mentions her in the bargain! 
I also like Socrates. Perhaps pronounced with a long o and a, in honor of Bill & Ted. 
Ozymandius seems like a good cat name.
You can call him Oz or Ozzie for short.
Atticus Catticus.
How about Feta? Or Hummus? I’m not sure if hummus is exactly Greek, but it would be perfect for a kitty with a loud purr.
Maybe just the letter mu?
oh, cmon people… call it…
Oedipus
My daughter’s cat is named Achilles. He has white mittens and stockings, and has a black splotch on one of his ankles.
Or you could see if Pepper Belly will fit the cat. It’s not Greek, but it’s a great name for a cat, as decided in the CS thread of the same name.
Odysseus, of course. The wanderer in search of a home (and my favorite person from Greek mythology). I’d say that fits your kitty. Oh, and if there’s no pics in 10 days, I’m sure Athena (Odysseus’s patron goddess, not the Doper with that name) will be greatly vexed with you. (As will Hermes, I’m sure.)
If it were a female cat, I’d go with Hecate. For males…Sisypuss?
If it is a black cat, then you must name it MORPHEUS.
How about a Greek place name? Athens, Thessaloniki, Piraeus, Patmos, Crete, Euboea, Lesbos, Chios, Kythera, Antikythera. All of our current flush of cats have place names (though not Greek).
Xerxes.
Thracymicus
Seeing as how the fella’s going to be snipped after you get him, how about Antitesticulares? 
Stabby Nachos. Greek pseudo celebrity name, by way of the “Go Fug Yourself” site