Can I mention professors' names in the statement of purpose?
Your statement of purpose should be specific to yourself and your research interests, first. Mention names only when the owner's work is both relevant and pertinent to your research interests. As JeffE stated, 


  If you try to craft the bulk of your statements to different professors in different departments, the result will be much shallower, and therefore much less persuasive, than if you describe your own well-developed research interests.


Your statement of purpose should paint a persuasive and intriguing picture of who you are, and should not be a hodgepodge of famous names and those whom you want to impress. You are trying to sell yourself and your ideas. Mention those whose work you have both read and found relevant to your research (and perhaps cited in your own work), but avoid name-dropping solely for the sake of impressing those who may read your SOP. That said, you should tailor your statement of purpose to the specific department you are applying to. This may include mention of the work of individuals in the department, or those whose work has informed their research. How much of this you should do is a judgement call on your part, and you should lean away from appearing to name-drop for the sake of making an impression.