Hot Daddy and the Monkey Puppets
On the sitcom Full House, John Stamos played guitarist and lead vocalist Hermes "Jesse" Katsopolis. In addition to the band, he had his own club called "The Smash Club" and he ran the radio show "Rush Hour Renegades."
At one point, he gets so wrapped up in the club that he gets kicked out of Jesse and the Rippers and forms this second band.
See also Human Pudding.