Whether you call it “Jock-A-Mo” or Chock-A-Mo” or “Iko-Iko,” it’s one of the greatest of all New Orleans Carnival songs. James “Sugar Boy” Crawford, who recorded the original version in 1953, rarely performs these days, preferring to bask in the glow of his incandescent grandson Davell. “The only place I sing is in church no,” Sugar Boy confesses.

“Jock-A-Mo,” one of a select handful of truly memorable Carnival songs, has had multiple personalities over the decades. Originally r...