In the novel 'Neuromancer', what is the name of the AI that hires Case?

In the novel Neuromancer, the AI that hires Case is Wintermute. It recruits the disgraced console cowboy for a dangerous operation designed to break through the barriers separating it from its counterpart, another AI named Neuromancer.

Wintermute is one half of an advanced artificial intelligence created for the Tessier-Ashpool family. The family’s legal and technical restrictions prevent the two halves from freely combining, so Wintermute manipulates people and events to assemble a team. Case is valuable because he is a highly skilled cyberspace hacker whose nervous system has been damaged, leaving him unable to jack into the Matrix.

Wintermute offers Case a chance to restore his ability to enter cyberspace, while also placing toxin sacs in his blood to ensure he completes the assignment. Molly Millions joins the operation, and the team eventually travels toward the Tessier-Ashpool stronghold in the orbital habitat Freeside.

Neuromancer is not the same AI as Wintermute; it is the other half of the divided system and is associated with memory, personality, and the preservation of human consciousness. Maelcum is a shipmate and ally, while the Dixie Flatline is a stored human construct. Wintermute is therefore the single canonical answer.