This NY Post article, reporting the sale of the New Jersey Nets to a rich Brooklyn person Bruce Rattner, who intends to move the team to Brooklyn, mentions that the New Jersey Sports Authority will ask the NBA to allow it to keep the name NEW JERSEY NETS (lucky for them that Nassau County didn’t pull this when the Nets moved to Jersey).
Background on the ownership of trademarks when sports franchises move, here.
The New Jersey Nets trademark appears to be owned by New Jersey Basketball, LLC.
The domain name NYNETS.COM was registered to a Long Island resident in September of ’02.
The domain name NEWYORKNETS.COM was registered to a Texas company in July of ’02.
The domain name BROOKLYNNETS.COM was registered by DirectNic in August of ’03.
Some will recall the Golden Age of New York -ETS names, 1975, when there were the NEW YORK METS, JETS, NETS, and, blink and you missed them, the World Team Tennis League NEW YORK SETS.