On one hand, I didn't realize Cal was the same school as UC Berkeley until Texas played them in 2015 (before I became a total cfb nerd), so I understand the desire to alleviate confusion.
On the other, they botched a rebranding effort not that long ago and I totally foresee the students rebelling against this, too.
Also, while I've always referred to the school as "Cal Berkeley" anyway, I was under the impression that was frowned upon -- that it's either "Cal" or "UC Berkeley" but not the two smashed together.