When Tom Benson bought the New Orleans Hornets, he gave immediate notice that he wants to change the name. He specifically mentioned that he wants the name "Jazz" back. The Utah Jazz were originally the New Orleans Jazz before their relocation. That's why the Jazz are named something that does not fit with their region or culture in any way, shape or form. 

There's been conversations about how much and what kind of compensation the Jazz would want in exchange for the rights to the name. A first-round pick? Money? Beignets? Turns out the answer is a simple "Nothing is enough." As Utah owner Greg Miller said on Twitter:

So much for that plan. It makes sense, it would cost the Jazz way more to have to completely redesign every piece of merchandise, signage, gear, and branding they have, plus the effect it has on the strength of their brand, and the impact on fans who would all of a sudden be wearing someone else's jersey. There's just no upside to the Jazz going through it. 

So New Orleans will have to make a different name. And that will be fun. Maybe then the Bobcats can become the Hornets again.

I still say the best option is a three-way swap for Memphis, Utah, and New Orleans. But its' also not my money.