The only reason why I would prefer that we did not lose the association with the name Berkeley on the academics side is because of all the historical references to the University of California in existence that used Berkeley instead at the time. Even in popular media and in films like Oppenheimer there are references to the university simply as 'Berkeley'. If that association is lost in the future perhaps those references will not be attributed to the university and thus it will not get the credit it deserves for past contributions to the world.
I could see someday, when this confusion is resolved, both the academics and athletics become California, like Michigan, Texas, Wisconsin, etc.
The only reason why I would prefer that we did not lose the association with the name Berkeley on the academics side is because of all the historical references to the University of California in existence that used Berkeley instead at the time. Even in popular media and in films like Oppenheimer there are references to the university simply as 'Berkeley'. If that association is lost in the future perhaps those references will not be attributed to the university and thus it will not get the credit it deserves for past contributions to the world.