Are you allowed to put a band name in the story you are writing?

You can use the name of a real band or solo artist in fiction, so long as you don't malign them. If your characters react in a neutral or positive way, you're fine. If your plot requires the band be awful so your characters can react negatively, or needs the band to be evil in some way, you'd better make up a band name and be sure no real band with that name exists. (Best bet: Make up a first and last name, plus a band name, like Maryn Bittner and the YA Questioners.)