step of giving up its brand equity and changed its name to the Big 10. With a coast-to-coast country, the name "Western Intercollegiate Conference" was geographically inaccurate. Whereas earlier the midwest of the country was considered the west of the country, the name was no longer accurate. Despite any name equity that was built they decided to leap forward and try something new.
Also the Big 10 has not lost any of its members, let alone its leading members, so keeping their name would make more sense than it does for Big 12 to keep its name.
But if the Big 10 expands further to 20 or more teams, I could foresee them changing their name as well.