Musk has used his Twitter account to pull pranks and make baffling changes in the past.
The new handle name, if it means the site, Daddy.com, is a website for new or expecting fathers.
The account remains active after the post. When he was later asked by reporters why he made the change, he confessed: "I was just playing the fool on Twitter". The final message culminated a unusual weekend for the billionaire chief executive in which he deleted tweets criticising Tesla co-founder Martin Eberhard and garnered backlash for comments about crediting artists online.
Although it is not possible to delete your Twitter account instantaneously, it can be deactivated within minutes and is permanently removed from the system after 30 days.
Elon Musk is never very far from the tabloids. Musk and Tesla each paid $20 million in September to settle with the SEC.
Tesla did not respond to a request for comment from Business Insider about the tweets in question.
Twitter got Musk into trouble again in February when the SEC alleged a tweet about how many cars Tesla will manufacture this year represented another misleading statement and sought to hold him in contempt of court for violating the settlement.
But Mr Musk sees the mention of Mr Eberhard as a point of aggravation.
That resulted in a new settlement that is supposed to put even tighter controls on his tweets about the company.