From the beginning of the Matrix trilogy, Agent Smith addresses Neo as Mr. Anderson, and Mr.Anderson only. He seems to be the only one who does so. Even the Architect addresses him as Neo, rather than Mr. Anderson.
Why does he refuse to call him Neo?
It is his slave name, name in the system. Thomas Anderson. Agents are pure, the utmost visible representation of the system and repression in it. Smith represents all agents.
Think of them as bureaucracy. You may have a nickname, everybody who knows you uses it or your first name. Lets say your name is Thomas and nickname is Neo. You got all your friends to call you Neo, because you dislike Thomas name and Tom nickname. But for tax services and other representatives of the government, you will always be Mr. Anderson whenever they have to interact with you. For them, you are just a number, for all intents and purposes they have with you, your first and last name will suffice.
It is indicative that they use Mr/Miss/Ms -Last Name- when they say "We have a deal, Mr Reagan?" to Cypher during their chat. It is purely professional sort of speaking, all work no play. You are Mr. -Last Name- who likes to call himself -Nickname-. We have you in our system as Mr. -Last Name- , by calling you anything else we would be getting too personal (towards you). And why would a bureaucracy/machines want to get personal with anyone?
I'd add that the mere meaning of "neo" as a prefix is exactly opposite of Agent Smith's drive - Keanu sought out a new world, Agent Smith wanted to rule the old world. They were polar opposites - even acknowledging his "alias" as who Keanu is, which isn't his alias after 15min into the film, would be to accept, at least a very small portion of Keanu's will to bring the new world. Agent Smith can't refer to Keanu as Neo within the system if he wishes it to maintain and cohere.
