I don't mind telling people I'm a college professor. I don't mind telling people the discipline I teach. But I definitely don't like telling people at which university I teach. You've got that info & you've got my name, my email address, a picture of me from the dept website, the phone number where I can be reached about 12 hours per day, and access to a whole bunch more info about me. That is way more than I want some stranger on a plane to know.
I suspect you're asking because, by golly, we could talk basketball, but the fact is, I don't give a hoot about my university's sports teams, so I'm not going to be worth talking to about that anyway. I really object to that probing, as innocent as I'm generally certain it is. I'm to the point of fibbing, but I don't really like falsehoods either. So much easier if people would just figure out some limits. I don't mind talking to some seatmates (depends), but personal info is personal info.