The point is, the name of the DoD is still the Department of Defense. Just like his dumb ass calling the Gulf of Mexico the Gulf of America didn't change the fact that it's still the Gulf of Mexico. All it meant is him wasting money on new letterhead to sooth his fragile ego.
He can make the executive branch call it The Dumpty Bowl if he wants. That doesn't mean he has renamed it. He has zero power outside the executive branch. Fortunately the United States isn't yet ruled by decree.
The names are decided by the United States Board on Geographic Names, which is under the Department of the Interior, which is part of the executive branch. So yeah, he can make them rename it for the US. Sure, you can pedantically say that he can only force the entirety of the federal government to respect the name, and the State governments could refuse to abide by that, but what would be the point? AFAIK none have outright refused. And obviously private citizens can call things whatever the heck they want, though if they get too creative they may have trouble expressing themselves in a way that others will understand.
The point is accuracy. He literally can only mandate the federal government. Everyone else knows it's the Gulf of Mexico in every state in the US and every English speaking country in the world.
I haven't heard of any states bothering to reprint maps. They all know his whole clown show charade will be over in the blink of an eye.
You could pretend he has more power than he does, but what would be the point?
