Can't you just get a Ph.D. in "Computer Science"? Or is that title not fashionable anymore?
My lab is not in the Computer Science department, we're in engineering. I am in the Graduate School of Information Science and Technology, Department of Information and Communication Engineering. That's why I get these two choices and no others.
There is a Computer Science department, but for some reason that's not how my lab is grouped. Why that is, nobody knows I think.