Raiden was always the real way to spell the name. But once the home systems came out they had to change it to Rayden because of the shooter game Raiden. The arcades continued to call him Raiden, I believe it was the MK4 home versions which finally switched back to using Raiden instead of Rayden. It could have had to do with Acclaim as well because they did all the MK ports before MK4.
