I think the full name is/was the PlayStation-X, but the X got dropped off somewhere along the line and only hangs around in the abbreviated PSX form. I'm not sure exactly where the "-X" stopped being used, but it might have been during the time when the system went from being the intended Super Nintendo CD-Rom add-on it was planned as to the stand-alone machine it eventually turned into.
"What an incredible Cinderella story, this unknown comes outta no where to lead the pack, at Augusta. He's on his final hole, he's about 455 yards away - he's gonna hit about a two-iron I think. Oh he got all of that one!