The name (Quadrophenia) is a variation on the incorrect popular usage of the medical diagnostic term schizophrenia as multiple personality disorder to reflect the four distinct personalities of Jimmy, the opera's protagonist.
Each of Jimmy's four personalities is supposed to be associated with one of the four musicians in The Who. The liner notes illustrate this concept as follows (names added):
A tough guy, a helpless dancer. (Roger Daltrey)
A romantic, is it me for a moment? (John Entwistle)
A bloody lunatic, I'll even carry your bags. (Keith Moon)
A beggar, a hypocrite, love reign o'er me. (Pete Townshend)
In addition to describing a personality/band member, the four descriptions refer to four theme songs that portray Jimmy's personalities in the opera: "Helpless Dancer", "Is It Me?", "Bell Boy", and "Love Reign O'er Me".
https://en.wikipedia.org/wiki/Quadrophenia
