You can only appear offline in Modern Warfare 2 and Warzone 2.0 if you're playing on PC via the Battle launcher. There is currently no way to appear offline on Xbox or PlayStation consoles. This feature has been included on consoles in the past, so could be added in the future.

In Call of Duty: Modern Warfare, players will be thrust into an immersive narrative spanning the entire game. Experience the ultimate online playground with classic multiplayer, or squad-up and play cooperatively in a collection of elite operations accessible to all skill levels.