Okay, so I haven't actually transitioned yet, but I'll play this game.
When I first realised I was trans, I chose the name Sarah Hart, because Buffy was Sarah Michelle Gellar and Sabrina the teenage witch was Melissa Joan Hart... I was really into those shows back then.
Nobody ever called me by that name, because I never really mentioned it. I did tell one female friend who knew I was trans that I'd like the name Sarah. She told me to pick something a bit more unique, simply because her name was unique.
I disregarded that comment, but years later I came up with a character for my first book, named Passion. She was a Goddess. So I toyed around with being called Passion. It didn't stick.
But Passion the Goddess was based on Hecate the Goddess, who I was familiar with from my Pagan days (right around the time of Sabrina and Buffy). Hecate was my favourite. Anyway, a couple years ago, I decided I wanted to open a gothic clothing store (if I ever could afford it) and call it "Hecate Black".
Cue this year, when I decided to drop the "he" and call myself "Cate Black". It plays right into opening the store, it's a perfect name for my books (especially the lesbian vampire erotica) and it reminds me of Hecate.
I'm not sure if I'll change my mind yet again or not, but at the moment I'd be "Cate Black" and that's good for me. And yeah, that's how I came up with the name.
Still no middle name, though if push came to shove I could just use Sarah as a middle name, because I'm still a huge fan of Buffy.