I may give them my name. And my parents' names. And ask them if they happen to know any of my family -- did you know my grandparents? Here's where they were born, and where all my cousins live now, and here's all the family history and gossip. And here's my shoe size, my girlfriend's favorite movies, my mother's best recipe, and I'll describe which dresser drawer I keep clean socks in, and, and, and...

If they want personal information about me, I can certainly give them a wealth of information that won't compromise my security but would hopefully bore them into submission.