I'd say it's more a kowtow to his voters and democracy. Whatever you think of him, he was democratically elected. Do remember to show up this November, though, and remind all your friends..
The president can not unilaterally rename the Department of Defense to the Department of War without approval from congress. Just declaring it so is not democracy. Those that call it the Department of War are enablers.
Capitalizing everything is the new direction, but I doubt it’s going to stick around. There’s a long legacy of DoD vs DOW, for a current military example that wasn’t updated: https://dodtap.mil/dodtap/app/about/DoDTAP
Here the DoD pattern makes it clear what part of the larger acronym is representing.