They actively use the name https://www.war.gov

Changing a domain name doesn't actually amend federal law.

Just like how changing Kennedy Center letterhead to Trump Kennedy Center for a year didn't actually legally rename it.

Once a case with sufficient standing got in front of a judge it reverted to the actual legal name on the basis that only Congress can change the statutorily defined name.

Yea, but by law the name change must come from Congress which it hasn’t. So it’s still The Department of Defense legally.

For an admin so obsessed with legal names instead of chosen ones, you’d think they’d be less hypocritical.