I've of the opinion that the letters don't actually STAND for anything, as is the case with postal codes (the Canadian equivalent of zip codes, for those who don't know).
In American usage, the N doesn't stand for anything as far as I can tell; it's just the letter prefix used for United States craft. Some countries have prefixes that stand for the country name, like JA for Japan (although their own name for themselves is Nihon), but apparently not the US. However the second letter does usually stand for something. Commercial craft are NC, gliders are NG, etc. Experimental craft actually are N-X. Although the second letter isn't considered a part of the registration per se, just a category designator.
Not sure we'll ever get a sensible explanation of what the USS is. Yes, I know they may have said "United Space Ship" or "United Star Ship" at some point, but what exactly is united about it? Like the concept of no money and of synthehol, it may be best not to look at that too closely.
I take it as being short for U
nited Federation of Planets S
hip. Just as the American "USS" is short for "United States Ship."
Personally it bugs me that the usages of an interstellar, interspecies, multicultural Federation are really just American naval or aviation usages. But it's what we're stuck with.