How safe/secure are chat rooms/IMs?

I was in a Yahoo chat room and got into an argument with a guy about something semi-political. About a half hour later I got a weird call at home, from someone asking for me by a version of my screen name, so it wasn't a random telemarketer. Also at an off hour. Could angry dude have found me somehow? I thought I was pretty anonymous in the chat rooms & IMing. NO? TY