The game in various forms is known by different names geographically, including the following:
Nocky door neighbour (Newcastle, United Kingdom)
Nocky nine doors (United Kingdom)
Ghost Knocking (United Kingdom)
Knock Up Ginger (Herts & Beds area, United Kingdom)
Knock door run (United Kingdom)
Knock a door, run (United Kingdom)
Chappy / Chap chap runaway / Chappy door run (Scotland)
Ding Dong Skoosh (West of Scotland)
Doorabella (Kilwinning,West of Scotland)
Thunder and Lightning (from "Knock like thunder, run like lightning" - United Kingdom)
Ding dong ditch (United States, Canada)
Chicky melly, chickenelly, chap door run (away) (Scotland)
Knock and run, and the similar knock knock run, and knock-a-door-run, both phrases used commonly in Great Britain.
Cherry Knocking (United Kingdom, late 20th century)
Rat-a-tat ginger (Shirehampton, late 1960s/early 1970s).
Nicky nicky nine doors (Canada, United States)
Ring and run (United States)
Knick Knack (nic nac) Earliest known reference in Ireland.
Knick Knock (Ireland)
Doorbell Ditch (United States)
Nigger Knocking (United States) 
Knock Knock Zoom Zoom (United States)