Q: What do you call the film that forms on top of pudding? My mother always called it "Mother."
A: I'm not sure if there is an official name, although it is often called a skin.
"The Oxford English Dictionary" "Shorter Edition" defines skin as "a film resembling skin on the surface of a liquid."
Since a pudding starts as a liquid, that works.
However, the term "mother" can mean something that grows in a fermenting liquid. Mother of vinegar, for instance, is a growth that can be used to start another batch of vinegar.
Since you don't remove the film from pudding to start another batch of pudding, it would seem that mother isn't a good fit. But far be it from me to contradict your mother -- my mother would skin me for that.