My last name is on my IMs when I send them. How do I take it off?

I can't figure out how not to have my last name show on my IMs. I sent my first IM a couple of days ago. I got a repsonse but the guy knows my last name now and he knows who some of my family members are. It's a little strange because our daughters went to the same high school. But I can't IM anyone else because they would have my last name as well. Can someone PLEASE help me figure this out.