Realize that you often won’t choose your actual dissertation supervisor until you are a couple of years into your PhD program. You’ll typically be doing classwork for several semesters before developing your own research project. You may be assigned an advisor or given a research or teaching fellowship with a faculty member from the start, but that person will not necessarily become your primary dissertation advisor.

Also keep in mind that focusing on a single faculty member in your personal statement can hurt your chances of admission unless you already have a close relationship with that person and know his or her situation well. Faculty members change jobs; they retire; they go on sabbatical; they take on funding opportunities that make graduate advising difficult; they die. It’s also possible the person you have singled out is disliked by the people reading applications or has such a high advising load that the graduate admissions folks are reluctant to admit yet another student interested in studying with that person.

You’re better off mentioning a few names of people whose work excites you. Do your research of the faculty. The PhD program is trying to enroll a class that has interests spread across all of the department’s faculty. Read faculty bios. Check out their publications. Find out what the new hires, Assistant Professors, and future academic stars are doing. The graduate program will be excited to find an applicant who is eager to work with the new and less-known members of the faculty. 

This approach is more than an admissions strategy: you may find that you have a much better graduate school experience working with the newer faculty than if you work with over-committed Professor Famous.