No, it's not. As your quote says, the Department of Defense was created by Congress; the President has no authority whatsoever to rename it or designate a secondary name for it. Writing the words "executive order" on a document doesn't make it legally effective.

Any citizen, of course, can use whatever fake names they'd like for people or places or government organizations. It's a free country. But I don't see any reason to choose this particular fake name except for the purpose of delivering propaganda to your readers.