In an official interview with Ed Boon, featured over on Playstation's blog Boon revealed the genesis of Rain.
PSB: Speaking of Rain, he was originally hinted at in Ultimate Mortal Kombat 3. What was the genesis of Rain?
Rain was me being a jerk, basically. [laughs] When we were working on Ultimate Mortal Kombat 3, I was thinking “what ninja color have we not done yet?” … and I’m a huge Prince fan, so I was thinking Purple Rain. I was probably still listening to the album. There was no time to actually make a character, because the game was done. So I hacked into the attract screen a quick little sequence of this purple ninja running at Shao Kahn. We didn’t even have the word “Rain” in the powerbar, so I manually built it using our font. So I included this quick glimpse just to drive people crazy. Once Mortal Kombat Trilogy came out, we gave Rain new moves and he finally became a real character. Later we brought him back for Mortal Kombat Armageddon. That’s one of the things about Mortal Kombat: many of the characters have these goofy development histories. Noob Saibot, Reptile…all of these odd origin stories.