The process takes approximately two years to complete, and any name change must be approved by the NBA's board of governors.
At this point there's no guarantee the change will be significant -- there's a possibility that the team will simply change "New Jersey" to "Brooklyn" and leave "Nets" as-is.
Americans and NetsThe franchise joined the ABA in 1967 as the New York Americans. But pressure from the New York Knicks made it difficult for the team to find a home venue in the city; they played their inaugural season in Teaneck, New Jersey and were generally known as the New Jersey Americans though "New York" remained their official designation.
A booking problem in Teaneck forced the Americans' first playoff game to be re-located to a venue in Commack, Long Island -- but the court there turned out to be unplayable and the game forfeited. Despite that, the franchise set down roots on Long Island, changing its name to the "Nets" -- both as an obvious basketball reference and for the rhyming connection to two other franchises popular on the Island -- baseball's New York Mets and the NFL's New York Jets. Their time on Long Island was the most successful in franchise history, as the team -- led by hall-of-famer (and Long Island native) Julius "Dr. J" Erving won ABA championships in 1974 and 76.
The team joined the NBA as part of the NBA/ABA merger in the summer of 1976. Before the 1977-78 season, they returned to New Jersey and were re-christened the New Jersey Nets.
Brooklyn New Yorkers?
Some detective work by the NetsDaily blog uncovered a number of trademark applications and Internet domain registrations for something called the Brooklyn New Yorkers. Will that turn out to be the Nets' new name? That's unclear at this point -- team management has denied any connection to the applications.