It looks like Call of Duty is just going to be known as "Call of Duty" going forward, as Activision Blizzard is rebranding Modern Warfare 2 and Warzone under a single, more generic header - at least on PC.
Across both Steam and Battle.net, the game client formerly known as Call of Duty: Modern Warfare 2 is now simply called Call of Duty. In an announcement on the Battle.net change, the devs say "this should make deploying to the battlefield even more straightforward, so you and your squad can worry less about where to launch and more about how to score your next victory."
So, to clarify, Call of Duty: Modern Warfare 2 and Call of Duty: Warzone already existed in the same client, and that client will now just be called Call of Duty going forward, with separate options within for both Modern Warfare 2 and Warzone. Remember that this is the Warzone that used to be known as Warzone 2, distinct from the original Warzone, which is currently known as Warzone Caldera, but is set to shut down in September. I think it's pretty clear why this name change is happening.
It's unclear whether these changes will hit consoles, as the store pages on both PlayStation and Xbox still refer to Modern Warfare 2 and Warzone. It's also uncertain what this is going to mean for future Call of Duty games. We know that Modern Warfare 3 will be revealed in a Warzone event soon enough, but will this year's game also be part of the existing Call of Duty client? I guess only time will tell.
The rest of the best Call of Duty games continue to live in their original, separate clients.