It's Twitter. It legally owns the trademark "Twitter", the bird logo and the color blue. Musk really screwed up that one huh? Under UDRP rules it'll be pretty hard for them to seize their rightful domain name twitter.com, but maybe they'll manage.
Their USPTO is still pending, so we'll see. But yes legally they have good grounds to continue DBA as Twitter.
I guess I couldn't believe it. The LLM copy on that homepage is unbearable and amateurish.