Name the Story

A computer hacker with legal troubles is offered a way out of his predicament by a thin, very dangerous woman and a cryptic-ass dude. He goes along, and hooks up with the woman along the way. Parts of the story take place in a purely digital cyber-reality called The Matrix. You can enter it by plugging stuff into your head. Another part of the story takes place in a futuristic Rastafarian enclave called Zion.

The guy is not called Neo.

I am re-reading Neuromancer and it's a funny experience. I read it back in the day (published in 1984) and recall it being edgy and challenging, but today it is very much in the classic mould... little distinguishable from THE STARS MY DESTINATION or any number of Phillip K. Dick books.

A somewhat better book than it seemed to me in it's time. Remarkably accessible to a modern reader (unlike some Gibson)