My college degree is BS Computer Science major in Computer Engineering, i.e., a Computer Science degree but with Engineering subjects and thesis. This is a top program that has more units than the usual Computer Science programs in other schools.
Nobody is preventing you from taking Computer Science and Computer Engineering separately, but it would be wiser and cost-efficient to choose what you want to prioritize because you will most probably never use both of them in your career (simultaneously or one at a time) as you specialize in your career. In fact, I didn’t use both of them at work.
In addition, you can always self-study whatever knowledge gaps you will encounter after college anyway. Your college subjects don’t have to dictate your career path. Learn anything now, and learn anyway even if you made the “wrong” choice.