You should refer to the character based on your POV character, who would be the eyes and ears of the audience. If this is third person, John and Mike would be known through their relationship with a POV character (David). If your narrator is first person either as a character in a scene or reporting the details, this will follow the character's natural storytelling skills, so the character will likely refer to John as John until it's time to call him Mike. If you are working in the Third Person, then your narrator voice is either limited-omniscient (usually will be aware of one character's thoughts and senses and can relay those to your reader), omniscient (knows every detail of the story from the moment it begins. May break the fourth wall and talk to the audience. Will have a first-person ability to with-hold the facts until the right moment to reveal) or Roving Camera (typically used in stage plays and filmed stories, where the audience is not privy to the inner thoughts of any characters and knows only that which occurs "on screen" or is said to have happened off screen. Will also follow a singular POV character through each scene but is not as impenitently aware as a semi- or fully omniscient narrator. It's like watching CCTV with sound. Could be used if you want the revelation that David picked up on a subtle clue that "John" was not John (Of course I believe you that you didn't kill Sue, you were with me when it happened... except you said 'I was with you when Sue was poisoned'... I never told you how Sue died, did I?).
Either way, you should refer to not!John as John until the audience learns that not!John is really Mike. After this point, the narrator should refer to not!John as Mike until John is back in his real body OR a First Person narrator or a character with Dialog with not!John refers to Mike in a way that acknowleges the situation's weirdness. A sarcastic character or narrator given agency and awareness of his status as Narrator and of the Audience may crack wise about Mike in John's body in so far as it fits his character.
Edit: Track down the Animorphs series if you can, which has a first person narrator (rotates between characters but usually is consistent within a book) and faced enemies who were mentally not the people associated with their physical bodies. Book six is especially a good read because the narrator actually becomes a victim of this, so his friends reactions to the reveal are told from his POV, rather then his own.