It's a first-class booking code on at least some airlines. Sometimes a restricted-F. IIRC, most of the coach "-UP" fares pull from P inventory on airlines that use it. But in this context, the OP may be talking about an airline where P is used more widely for the first-class cabin as a whole.

If I knew the agent because I was a frequent flier, it would not creep me out if they greeted me by name. I've gotten to know gate staff at my home airport over the years. But I would be highly disturbed if they were conducting background investigations on me without my knowledge and using data mined from the Internet to compose a dossier.

I've heard of hotels doing this as well. We had a thread here about a hotel in Minnesota that was exposed for conducting investigations on their guests...some run-of-the-mill Westin or Sheraton IIRC...