the name comes from the following:
Purple: because the drink is purple in color
Jesus: because you will get so drunk you may see jesus
Rodeo: because you'll be so hopped up on energy drink and caffeine tablets that you may be prone to jumping on your friends and riding them around like you're in a rodeo
GUY #2 dude you drank one Purple Jesus Rodeo and starting running around the party jumping on people!
GUY #3 Yeah then you passed out and we had to take you to the hospital.
GUY #1 NICE!