Varies from school to school, but where I did my PhD, the degree was in chemistry regardless of what division you were in. My division was formally inorganic. My research was mostly physical. And my degree is chemistry. All the division meant was what classes you needed to take, and you could choose whatever you wanted. Classes were mostly meaningless anyway. So you could be in the chemistry department, biochemistry division, and your degree was in chemistry.
But to make things more confusing: my university ALSO had a biochemistry department. If you graduated from that department your PhD would have been in biochemistry. Some of the professors had dual appointments. These same kinds of overlaps are encountered with physics and material science as well.
My advice would be to inquire at the university you are applying to and see if they accept biochemistry b.s. In the overwhelming majority of cases they won't care - if you have the required courses, plus the required standardized tests, you could probably be an English major for all it mattered.