I want to say that the symbol should be something fancy like this screenshot from the original Legend of Zelda.
However, as countless corporations and franchises have demonstrated, symbols and logos get simpler over time. I guess this is because they want them to be easier to draw. The Legend of Zelda has pretty much already gotten to the simplest possible symbol: a plain gold/yellow Triforce. Sometimes you'll see the bird under the Triforce or the Master Sword behind the Hylian shield with the word "Zelda" in a special font, but you'll usually only find them on title screens, official art, and important items. Plain 'ol Triforces are much more common is is becoming increasingly common.