In the first Mortal Kombat, Ed Boon spelled his name "Rayden" so no one would confuse him with Fatal Fury character Raiden.
Raiden's name and status as a god are taken directly from the Japanese thunder god Raijin.
Raiden's design was inspired by one of the Three Storms from the movie Big Trouble in Little China. He was modeled after Lightning, of course.
Lightning from Big Trouble in Little China
Ed Boon confirmed in an interview that when Raiden does his flying push move, he is yelling gibberish and not anything English or Japanese. I'm a big fan of, "GET BACK IN THE CAR!!!"
Raiden was going to use his staff as a weapon in MKII, but it was omitted due to memory constraints.
Sources:
http://en.wikipedia.org/wiki/Rayden