In the adult timeline he became known as the Demon thief because he touched the Triforce and used it's power to turn into Ganon.
In the child timeline [specifically in TP] he's called the Demon thief even though [as far as we know] he hasn't turned into his Ganon form yet...this might be because the stories of his battle with the Hero of Time were known in the child timeline. We are told that the story was passed down through the Royal Family after Link returned to his own time and warned Zelda and the King.

__________________

Bomber's Notebook | Zelda Informer, Home of The Bombers | Theorizing Resources
Voted as Best Zelda Theorist in the Summer '08 Awards. Thank you to all who voted, and to all who inspired me along the way!