Both are right.

His name was originally Raiden, but when it came to making MK for the consoles, there was an issue with the copyright for the name as another game had the name Raiden. So for the home consoles for MK1-MKT, his name was spelled Rayden. But when MK4 came around, the spelling changed back into Raiden. Some people prefer Raiden while others prefer Rayden. When it comes to where his name is derived from, Raiden would be the correct spelling, but the actual pronounciation would be different.

Both, essentially. It's more of a time line issue in the sense that you're asking.

Around Mk1-2 Midway ran into legal issues around the then spelling (Rayden)...and from like Mk3 on, it was changed to be spelled Raiden.

yea, I'm pretty sure that's right...lol

From good old wikipedia:

Raiden's name is spelled Raiden in the original arcade iterations of the Mortal Kombat games, and in every game released since Mortal Kombat 4. The console ports released up until MK4, along with both movies and the Malibu comic book series, changed the name to Rayden. This was allegedly because of copyright issues as a shoot 'em up was named Raiden, or possibly to keep from confusing of Raiden from the Fatal Fury series, who was seen as a large wrestler.

From The Temple:

(he is spelled Rayden everywhere else but in the original game - there were some copyright issues with registering the name Raiden for the movie/animated productions)

My own two cents:

Most likely it was copyright issues that caused the different spellings. If that was and still is the case, then he'll be called Raiden in the games but if in a movie or other media then will show up as Rayden. Silly gods, they are always changing their names around just to confuse us poor mortals.