Originally Posted by
Ed Oscuro
They only have been doing that since 2004, so that part isn't relevant.
That said, you're right that I don't know of an instance where Sony themselves used the term. Nowadays when you go to a PlayStation site you see that PlayStation, the logo, and PSX (amongst other terms) are registered trademarks of Sony, but in the old days PSX wasn't a trademark of theirs.
Of course, that doesn't mean that they didn't use it in some informal capacity, or at some later time (before 2004).
I wish I knew how it got started; even so I agree with MachineGex that many original PlayStation users tend to call it the PSX.