I think they will be called the New York Nets. Peple in Brooklyn are going to root for them anyways, but being called "New York" will attract a lot more fans from the City and surrounding areas. In sounds sentimentally great to call them "Brooklyn" and it would be cool, but in these times where every thing is to much about money, I can't see them passing on the New York title. And the stadium won't be called "Ebbets" either.
Wouldn't, marketing-wise, it make more sense to have the name Brooklyn. There's tons of gear sold nationwide that has an NY or New York on it. The Nets would have the only gear that says Brooklyn across the chest.
Big, huge, giant money maker there.
Besides there is the whole nostalgia marketing end to it.
As for the name of the arena that is going to go to the highest bidder.
I happen to like Geico Arena myself with a billboard of Lebron playing a game of one on one vs the Geico Gecko hanging outside the arena.