What to say when a headhunter/recruiter asks what processes you're in

I'm currently interviewing for PE jobs for a near term start. Working with several recruiting firms on different processes. There's one in particular that I think is a golden egg and I don't want others to know about it.

So I took an intro call with another recruiter today, who asked what processes I'm in. I wanted him to know that I'm getting really good traction, so told him I'm in final rounds with some. He asked for names. I told him two of them, he kept asking. I was reluctant to say the third (the one I really want), because I'm afraid he'd use the information to reach out directly to the PE firm with a book full of new resumes. Am I wrong in assuming that's why he's asking? Getting info to see what firms are hiring? Like that Director in your group who tells a bunch of PE buyers he's intimate with a company pursuing a sale, when he's really not, but ends up bringing a bunch of interlopers to the table? Is that the way this industry works, or is there some type of exclusivity that my other recruiter has with this PE firm?

I just know there are some recruiters out there (Pinpoint, Mercury) that never actually have any mandates, but just phish for info so they can go try and line something up. (for disclosure, this isn't one of those two firms, this guy was from JHB, which seems legit). How would you respond to these types of questions?