Is it possibly considered weakness in my statement of purpose if I mention that I would like specific people to advise my PhD programme?
I would include which certain aspects of the faculty would support your intentions and why, especially if you can include meaningful references to their previously published work.

For example

"I believe that University X would be a great place to undertake my research into topic Y because it has a great reputation in this field. For example books A and B published by person C are well known texts in the field and I believe the research of person D in the area of E would compliment mine."