I remember seeing this discussion on this board several years ago, and i think we lost SJU and became STJ when St. Joe's in Philly took the name and they became SJU. Even though we are the older institution they made claim to the letters.
Actually, when I was a student at SJU, St Joes was a college, not a university, and they were SJC at the time. So them having the SJU letters is rather recent.
St. Joes' was simply faster to the draw in registering the internet domain. In the early days of the internet, enterprising geeks registered common corporation names and then tried to sell them back to those corporations. When it was sort of generic - like delta.com for delta airlines, the companies would be more inclined to pay for them. When they were directly names of a well known company, say a Macys.com, those companies generally sued and won if the pricetag to buy the domain name was too high.
St. John's discovered the internet about the same time as a WWI Japanese solider hiding in a cave on Iwo Jima for 65 years did.
I am guessing SJU rebranded to STJ with fears that potential applicants entering www.sju.com thinking st. john's, weren't instead driven to the st. joe's website.
Yeah, my old organization paid quite a bit for Australia.com.