In reply to: it would depend what is registered with the secretary posted by jt
either way, I cannot imagine the Pac 12 giving up their rights to the conference name with a significant amount of compensation.
schools? Even if it's only like two schools, through the commissioner acting as their executive acting at their discretion, they could negotiate a deal with the Mountain West or the West Coast Conference or whatever takers they have to merge assets and retain the Pac # name. The remaining schools would have an incentive to do this because the Pac 12's brand power is greater than whatever conference they would merge with.
If all Pac 12 teams bolted, I assume the organization would dissolve as there'd be no income to pay for administrative staff. With no one to use intellectual property to keep its protection, given its substantial intellectual property at issue that would be up for grabs, I'd guess a receiver would be appointed to deal with the assets. And there's a decent chance a pacific coast conference would be interested in picking this up. Which is why the remaining Pac 12 teams should want to try to leverage that early on rather than bolt for a lesser conference.
I thought I had made that point; my assertion is that someone can't just look and say, "hey, no conference anymore, we can just take that name!"