I don't know any other name for it, but it's pretty popular in our school. Someone starts with a story and the next adds another sentence to it. We've always ended up with some pretty funny stuff.
Just to prevent confusion: Things like "I'm here!", he said and went again.
count as only one sentence.
So, let's start:
It was a normal mid-summer morning in Ankh-Morpork and the weather was miserable.