What does NSX stand for? Nintendo Switch Xtreme? Maybe not Xtreme...the 90's are over... For that matter, why do some people call the PlayStation PSX instead of PS or PS1...And what about GCN? Game Cube (from) Nintendo? Game Cube Nonpareil?
Nothing personal, I just need answers.
I used to follow this sort of 'naming convention' when it came to systems, and I could be wrong because I haven't followed this sort of thing much in recent years, but here is my understanding of what you asked about:
1--PSX. Put simply, I believe PSX was the code name used for the original playstation while it was still in development.
Obviously, it was just called "Playstation" upon release, but for the sake of abbreviations, most gaming magazines at the time, followed by gaming fans, simply left the 'PSX' name in place.
For some reason, and I think this all DID start with the popular gaming mags (EGM, GamePro, GameFan, etc), there seemed to be some unwritten rule that ALL game systems needed to be abbreviated using a three letter/number system.
PSX, N64, SAT (or sometimes SSA), XBX...you see where this is going... which leads to...
2--GCN. I think you answered your own question (again, I could be fuzzy on this nowadays), but GCN simply stood for Game Cube Nintendo. I have also seen the Gamecube abbreviated as NGC.
3--As for the Switch, I believe the development name, or codename for it (like the Playstation) was simply NX. Upon release, we now have the Nintendo Switch, and because, it seems we NEED to have a third letter/number, leave the X in there...thus NSX.
I hope that satiates your need for answers.
And hey, even if I am not 100% right, I thought it was a rather damned good explanation, no?