There is but one question: why?
Don’t you go to hospitals and clinics to be free from pain? You don’t go to a clinic to suffer from more pain. Wouldn’t a “Pain Relief Clinic” or a “Pain Cessation Clinic” or a “Pain Mitigation Clinic” or an “I Am In Pain And Want It To Stop Clinic” make more sense?
True fact: there was a copy of Dante’s Inferno on one of the waiting room tables.
Nishiryu 
I agree we need to overcome pain, must deal with it and not encourage pain.
I was so taken with the sign that I went back to take the photo. I should be complimented for not engaging in my usual flights of fancy on what Pain Clinic really did.