Third Person (Limited Omniscient): Case
Neuromancer is told in a third person limited omniscient narrative voice. Yeah, that's a ridiculously long name, isn't it? Thankfully the idea behind this name is pretty simple. Basically, third person limited omniscient narration means the story is told by at outside narrator who tells us the actions, thoughts, and feelings of just or two select characters. In Neuromancer's case, that character is Case.
Let's break it down with an example: "[Case's] brain was deep-fried. No, he decided, it had been thrown into hot fat and left there, and the fat had cooled, a thick dull grease congealing on the wrinkled lobes, shot through with greenish-purple flashes of pain" (11.14). Notice how we get Case's feelings (hung over) and his thoughts (he decided). However, Case isn't giving us the information himself (if he was, it would read "I decided"). Instead, someone else—i.e. an unknown narrator—tells us what's going on with Case.
That allows us to keep a healthy distance and see Case for who he really is—a deeply troubled dude with a serious drug problem. And yet it allows us to get close enough to him that we can't help but root for him, despite his less than savory qualities. In that sense, it's a great way to narrate the story of an antihero—close, but not too close.