Maybe obvious names such as Midnight, Blackie, or Spooky?
Sabrina Underfoot.
( I love the Underfoot thing. Brilliant!)
My friend’s orange-eyed black cat is Shadow. Suits her quite well. 
I’ve mentioned on these boards before that if I ever have a cat again, I will have two: a black cat named Spook and a white cat named Cracker. 
Sheba.
I have a black cat named Tiabbo (for Trouble In A Black Box). It’s pronounced tee-AH-bo.
I say don’t rush it.
If you resist the urge to name the cat right away over some time the cat will more or less tell you what it’s name is. It’s real name.
I’ve had two cats that we named only to have them both undergo a name change later on once we got to know them better.
…I have a friend who came to me with a nameless cat. I told her to name him Heinlein. His name is now Pooh.
When I told her to name the second cat Niven, she responded by naming it Ink. ('Twas a black cat, naturally.)
Four shiny new cat names for you to consider!
Pyewacket
I had a black cat named Boo, but I spelled it Bu. She had a sister named Tu.
Scarlett?
That’s why I have a cat named Mia. I asked her what her name was, and that’s what she said.
Not particularly, it was just my first inclination. It’s a nice name and it rolls off the tongue pretty well. Maybe I just think it’s pretty.
Personally I would avoid ‘Jade.’ Nothing against the name at all, but I’ve met quite a few cats with that name. It seems a bit over done, IMO.
Black female with green eyes famously describes one of my least favorite exes. In her honor, please call your cat, “Heifer.”
Thank you.
OtakuLoki: Those sound good. Kage especially is the right length and is plenty euphonious.
PapSett: It would always go for the eyes.
astro: I’ve considered that one.
John F: That is very possible. I once had a white male cat named Yowler because he was very vocal: He was probably part Siamese, and he was always talking.
Pythian Habenero: Naming it after a science fiction author sounds interesting, but it would probably have to be Bradbury. A black cat from the October Country, you know.
Biggirl: All those names have a certain charm.
Askia: Remember my distaste for naming cats after disasters? I think it applies here.
Fern Forest, Shirley Ujest: The Underfoot convention is apt as well, especially when I’m walking in the dark and the cat wants to follow me ahead of me in addition to doubling back and marking me with all her glands. It’s a wonder I don’t trip into a pile of fur and fangs.
Thanks again for all the names.
Well, I guess I’ll keep the name Cleocatra for myself then, since it seems beneath your notice.
Depending on how well-behaved the cat is, you can always go with Jealousy.
I name my cats after greek gods/godesses, with names ending with an -s. My green eyed female cat is named Artemis , with also sums up her personality very well: She’s proud, beutiful, and won’t let anybody – neither cat, man, or other – near her, except me. If somebody won’t listen to my or her warnings, they actually end up bleeding. My other cats are very friendly to anybody, but this one is just like, well, Artemis.
We have a small female all black cat, and that is her name. We just call her Pye for short.
I’m glad my cats attempts to kill me have come to some good. BTW, if you pluralize them Underfeet we shall be forced to call them the black sheeps of the family.
Tabitha seems to work well for my sister’s female black cat with yellow eyes.