WWE held ownership of Cody Rhodes’ name after he left the company. This is why he’s just “Cody” in AEW, and he was previously only called “Rhodes” when introduced as “Cody and Brandi Rhodes.” Brandi never went by her name in WWE because they called her Eden for some reason.
According to Heel By Nature, WWE has cancelled their trademark on Cody Rhodes’ name. That theoretically gives Cody an open door to call his attorney Michael Dockins and get another trademark going.
The company filed a cancellation notice for “Cody Rhodes” on November 2nd. This was a huge win for Cody as he has fought so hard to retain ownership of his name. WWE didn’t let go of properties like The Match Beyond, Bash at the Beach, WarGames, and so many others that Cody wanted. At least he can assumably get his name back.
Cody tried to register his name on April 13th when the trademark expired. Then WWE came back a month later and attempted to revive the trademark while blaming COVID-19 for the delay. It appears they finally gave up that fight.