A few bands who use avatars do embody the personality of their music, there are often called “mascot”.
GOZ from Shaka Ponk: Goz is a digitally-created monkey. He is the mascot of the band but is also sometimes credited as a band member. He can appear on stage during concerts and challenge Ion, the drummer, on a Drum battle.
The Guy from Disturbed: He is more like a mascot and appears regularly on the band’s covers. He can be the embodiment of the Archangel Gabriel.
We can consider Johnathan Davis’ microphone stand as an avatar too. It was designed by H.R. Giger himself. The microphone is always covered at the beginning of the concert and gets unveiled once the band members arrived on stage. Fans are always excited to see it in person as it his a great piece of biomechanical engineering and can move by being pushed and pulled by the singer.
Eddie (or Eddie the Head) from Iron Maiden: Extremely popular, he is shown on CD covers and all merchandising. I already talked about this but during live performances, Eddie becomes a member of the band when he appears on the stage as a giant robotic puppet.
You can now play Eddie the Bird in the extension of the “Angry Birds Evolution”. I love the character design and I can’t wait to try out the game ( playable character available for two weeks from 18th of October 2017).
There are also a lot of bands wearing masks or makeup to create different alter egos: Slipknot, Marilyn Manson, Kiss, Sia, Lady Gaga etc.