Caller ID issues

I have had my home phone number for over 3 years now, and I also have a business line installed in my home (18 months ago), but when I call anyone on either number (and it goes to a subscriber of another carrier (i.e.  Not Verizon), they see some OTHER persons names on the caller ID.     How do I get the proper name(s) to display?  Especially on the business line - I need my clients to see my name and not someone else from 2-3 years ago.