Right now, we have a lot of rift-raft in the conference. All the good schools (except us) have left. Whatever we name the conference, we need to make sure everyone knows we are not rift-raft like everyone else. We don't want people getting confused and thinking we are just another one of these awful, awful schools we are associated with.
That's why we need to make sure our name is prominently featured in the conference name. Something like "The Husky Conference" or "The Super America Conference Featuring Connecticut". I'm sure the other schools would go for it because they probably look up to us and admire us, etc.
Another name I think would be good would be "The Conference Formerly Known as the Big East". That way people know we used to be in the Big East and know how much better we used to have things. They might think we still are in the conference. We can tell people "Yeah, we're still really kind of in the Big East. It's kind of technical. It's really just a bunch of semantics. Everything is still okay."
