These are staged wrestling matches. He didn't "fight" for anything. He re-signed with the organization that owns the copyright to his in-ring name. So he can use it again.
For example: when Scott Hall left the WWE he couldn't use the "Razor Ramon" name, persona, likeness. But when he re-signed with the WWE he had the option but decided to stick with his real name and his NWO personification. You've stated twice that dude "fought" for the name and that's on some "It's still REAL to me dammit" ish. It's called a "story line" bro.
Im not sure about this particular event. But in Mexico some wrestlers do own their name. Mil Mascaras, Santos, Blue Demon among others. Rey Mysterio owns his name and gimmick, it is not property of the WWE, since the uncle is the original Rey Misterio.