The real story behind the name "501st" is rather unremarkable. I wanted something that sounded military, had a big number, and ended in a "one" to give it a little authenticity. I also wanted a number that would be alliterative if used in a motto, and I've always liked the motto "Fighting SeaBees" from WWII. Either 400 or 500 sounded good, because both began with a "f" sound. I liked 500 better, just because it's one of those nice round numbers. So 501 worked when I added the "1". The only problem was that, at the time, Levi's 501 jeans were still popular and I was taking a risk that we'd have that joke haunting us. But, luckily, I only heard us being called the "Button Fly Troopers" only once!
As for the "Legion" moniker, that's a different story. The original website was dubbed "Detention Block 2551" and was a simple little geocities site for folks to send in their pics in stormtrooper armor to be displayed. After we got enough people in there, it seemed like a good idea to make a fictional military unit, just as a laugh. My dad being a graduate of WWII airmen school, I liked the idea of a Squadron of fighter pilots. I always liked looking through his graduation book and seeing rows and rows of pictures of cocky pilots with their leather jackets and their rakish grins. But since stormtroopers are ground-pounders, the term "Squadron" didn't make sense. I truncated it to 'Squad' since that was an infantry term. I figured we'd always be a small, intimate group of hobbyists so I stuck with the small-scale unit name instead of something that sounded massive. Not long after that, however, it became obvious that we were getting way too big to be a Squad.
So I started thinking about what term we could use, but two problems existed concerning contemporary military unit names. Firstly, I didn't want to choose a unit name that would pigeonhole us at a fixed size. Secondly, I didn't want to disrespect the real military by putting on airs we were a real regiment, battalion, etc. My solution was to do what Lucas always did: tap into historical source material. Not only did it have the advantage of sounding more ominous, but it enjoyed the ambiguity that the passage of time lent it intuitively. I liked the idea of the old Roman Legion. It was very old word, sounded very distinguished, and even though it did have a fixed number it wasn't readily obvious in the contemporary context. When I re-watched ROTJ and noticed that Palpatine mentioned two of his "finest Legions" were on Endor, I knew we had something that had roots in the Star Wars universe. Problem solved! (...except for the fact that the Legions we see ended up being only about 3 score men—not an incredible number for a final battle! I've always wondered why Lucas re-did the trilogy without adding a thousand computer generated troopers in the Endor battle. Go figure.)
Lastly, I wanted a name for our regional chapters. I knew this club wouldn't survive long if everyone was paying tribute to the bigger club all the time. Eventually, local preferences would win out and independent-minded people would want to strike off on their own. The Legion would have a definite expiration date then! So I went back to the Roman Empire model of occupation and, considering we're pretending that the Legion is occupying puny little Earth, I felt that Garrisons would describe regional units created to occupy territories. The first three Garrisons were pretty simple: East, West, and Central. But they weren't called Garrisons until the map was divided a little more into big chunks of the U.S. The original Garrisons were: Eastern, Southern, Central, Midwest, Southwest, and Northwest as well as a European Garrison overseas. As you can guess, these units were carved up into more practical units quickly, although Central and Midwest remain to this day and Southern became an Outpost but will probably stay that way in name only now that it is of Garrison size.
Squads were resurrected as units of very local orientation. And the term Detachments (lifted from Vader's speech aboard the Tantive IV) was used to describe theme-based groups within the club. Since the detachment Vader sent to the surface of Tatooine probably consisted primarily of desert troopers, it made sense that a detachment would have a specialized orientation. Outposts made sense for remote areas. The outpost on Dantooine was referred to in ANH as well, so again we lucked out with a term from the trilogy.
So there you have it. The 501st Legion naming convention history in all its glory. I hope you've all stayed awake long enough to enjoy.