No, we do not require you to pick an advisor prior to entry. You have the first year to find a PhD advisor, which you do through courses, research rotations, seminars, group meetings and other contact. In contrast, some of our competitors force you to align with a particular advisor, whom you may have never met and whose work may not entirely interest you, before you begin.
Do note, however, that your graduate application will be stronger if you have some idea of what you want to do. If you do have such plans, please discuss them in your application statement. Try to be specific; simply listing the names of lots of professors, without providing concrete reasons for why you are interested in their work, is not likely to help your case.