Palliative band names refer to bands with names related to relieving or alleviating pain:

1. First Aid Kit

“Shattered And Hollow”

https://www.youtube.com/watch?v=hW_RLtnqY1o

2. The Cure

“Boys Don’t Cry”

3. Therapy? — an alternative metal band from Ireland

4. Band Aid — a charity supergroup featuring mostly British & Irish musicians

Let me know if there are any more that you can think of!