Looks like the name came from this comic:

Cyanide & Happiness was originally called Comicazi. The name Comicazi was being used by comic vendors, so I changed the name to Cyanide & Happiness based off the ingredients of back alley cotton candy in one of the earliest comics, as well as to reference Calvin and Hobbes. Couple months after that, Cyanide & Happiness was invited to be on Explosm.net.

So I don’t think this was the original, just an early one.