Yes, you certainly could raise a boatload of money in one fell swoop by selling the naming rights for the building; I've seen estimates up to $150 million. Unless you've got someone willing to name it after, say, Caruso or Flagstad or Mahler or Toscanini, it will leave a bad taste in everyone's mouths, just the way Koch Theater and Geffen Hall leave bad tastes.
David Gockley has managed to greatly increase the San Francisco Opera endowment and obtain donations of up to $40 million without selling the name of the War Memorial Opera House. He'll have some free time in less than a year, but I bet he can tell you how he does it over the phone. And he can probably help out with labor relations as well. That's been going nicely at the opera house since he arrived.
Also, Met? Keep in mind how well it all worked out for you with Alberto Vilar. What you might want to consider is staging operas that people want to see. A season as top-heavy as yours is on Puccini and Donizetti isn't going to get me in the door.