Check out the arcade games (MK1, MK2, MK3.. not UMK3 because he's not mentioned in that game I don't think, and MK4), which are THE definitive versions (at least in HMO! though of course people say that MKG trumps MK4, the one exception in that list). It's spelled "Raiden" and pronounced IN-GAME as "Ray-Den" not "r-eye" or any other variat thereof. If you want to really get technical I think MK2 rolls his "R" like a frenchman, but it's nothing close to "r-eye" !
The only versions of the game that spell it "raYden" are the console ports, and MK Trilogy (sadly, since it was never released in arcades).
I'm not sure about MKGold (haven't checked in awhile), Deadly Alliance or Deception (haven't played the latter too).
Since it's only the home versions that are different and it was done for legal reasons, not story reasons...
So it's spelled "Raiden" and pronunced like "ray-den."
Poor kids who didn't grow up with the series can't be blamed for not knowing the true Ol' Lightnin' Hat's name.