> why. unlike with the gulf of mexico, in this case they have full naming rights.

They actually don't. The official name is still the Department of Defense and only Congress can approve a real name change.

The Trump Executive Order just gives the department permission to use the Department of War name without actually changing the name of the department from the Department of Defense.

That said, despite being anti-Trump I'm fine with calling it the Department of War, it seems a lot more honest.