I don't think changing the name will change the "brand" on the Sunbelt. The name is pretty important to branding and it is hard to make a brand if you change the name.
"What conference is that?"
SBC has made great strides in Basketball and Football. Since UNT does not have a baseball program (yet) I don't know about that part of it. Other sports like track, softball, gymnastics are part of the growth too.
One change I would like to see is a larger set of schools in the major sports. UALR (if they have a football program), USA, Denver (if they have a football program) need to be in the conference for Football, Basketball, Baseball, Softball, Soccer and Track at least. Look at the Big 12, SEC, Big 10, Pac 12 - all of the member schools in football also compete in basketball, baseball, softball, swiming and diving, soccer. Once UNT gets a baseball team, we are pretty much in the SBC in all sports.