Thank you for the replies. They suggest I might not be crazy for thinking the way I do about this situation, which is good to know.

I haven't told the acquaintance the name of my psychologist (at least I don't think so). The thing is we go to the same place (but see different therapists) and it seems like he might want to change and see mine instead. It's quite a small place so I guess it's entirely possible he'd end up seeing the psychologist I go to. I'm thinking about telling my psychologist about this whole thing and how it makes me feel but I'm worried she's going to think I'm weird, too attached or simply out of line. I also feel guilty because what if my psychologist would be a "perfect fit" for my acquaintance and I'm denying him the possibility of getting some real help?