Yes, it's officially still the Department of Defense.
If this were a news outline writing "Department of War" I would be concerned. But in the case of the Anthropic CEO's blog post, I can understand why they are picking their fights.
It's a silly shibboleth, but I automatically ignore anyone who calls it the Department of War or Gulf of America. Hasn't steered me wrong yet. They're telling me they're the kind of people who only care about defending fascism.
They can, however, rename their Twitter/X accounts and vacate the @SecDef handle, which seems to be up for grabs now, if anyone wants to do the funniest thing...
Of all the silly things that Trump did, I think this one is the most reasonable. This has always been a department of war. Calling it defense was propaganda.