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?