I think you can stop with the name hunting, because a change just ain'y gonna happen!
I would be absolutely shocked if they ever changed it from the Big Ten. There is over 100 years of tradition in that name and it is easily one of the most recognized names in sports. They would have to spend a hundred million dollars in advertizing to get a new name anywhere near as easily recognized as "Big Ten" is now. It would be absolutely foolish to change the name.
If it can be the Big Ten with 11 members, it can be the Big Ten with 12 members.