ppmm

"The problem is that the department cannot give me the new professor's name until he/she actually arrives in the department this Fall." This is VERY sketchy. Departments are ordinarily happy to brag about new hires as soon as a faculty member has signed on the dotted line. They're also often willing to give a name, especially for recruitment purposes, when an offer has been made but hasn't yet been accepted. There are reasons for confidentiality during negotations, but I can think of no reason why either the department or the new professor would want to wait until he or she actually "arrives in the department in the Fall" to announce the hire. In fact, it would be almost impossible to keep the secret once the person in question had resigned from their existing institution, which they must do by May 15 of the preceding academic year. Sorry to say this, but I think what this probably means is that they intend to hire someone to replace your POI but haven't done so yet, and may not even have made an offer or begun a search; and if that's true, it doesn't speak well of their integrity that they're willing to misrepresent the situation for the sake of graduate student recruitment.