I strongly suspect that the shop on LSUSports.net has a business relationship with LSU and is giving them some sort of compensation. Thus, they have to play by the same rules as LSU. In fact, the shop could even be owned by LSU.
ok, to be specific, NIKE isn't allowed to sell them. in fact, no one is allowed to sell them with an active player name/number combo. it is also illegal for a mom and pop shop to add the name or number to a jersey that makes it a current player. only the NCAA will probably never even found out who the mom and pop shop is, so odds are they'll never get popped. but those stores advertising all over the net are easy targets, and would get nailed rather quickly if they were selling them.
If they are selling NCAA authentic merchandise, I would guess the NCAA has a governing rule over that, but not for just putting on names and numbers I wouldn't think.
If a store has a licensing agreement with LSU to make authentic LSU jerseys, then LSU requires them to follow NCAA protocol. But . . . there are sports shops without marketing arrangements with LSU. If you bring a jersey that you own into the shop and ask them to put a players name on it, they can. You can buy iron-on letters and do it yourself, too.
Rumor incoming.... I believe the only last name you're allowed to put on any 'licensed official NCAA jersey' is your own last name... as a personalized thing. I'm thinking Jones/Peterson/Jefferson/Sheppard/Scott should be fairly easy to explain... Alem might be slightly more difficult.
A NCAA licensed dealer cannot market and sell such a jersey himself. But YOU can put any name you want to on any jersey that you own. The NCAA is not the law.