Same concept used with Secret Santa during Christmas where everyone draws a name out of a hat and gifts the other person. Secret Jesus is used when participating with a Christian family primarily because Santa is believed to be of the devil and the gift exchange happens on New Year because Christmas Day is reserved for Jesus.
Person 1: "Hey, are you doing Secret Santa with your family this year?"
Person 2: "Nah, my family are fanatical Christians. It's more like a Secret Jesus gift exchange.