I am paying the designer for doing design work.  He should not expect free advertising as part of the deal unless it is negotiated up front.  I have the attitude that the advertising should cost a lot more than the design job

@EGOL, I couldn't agree more! I found myself in such situation when paid to web-designer to make a site. From a client point of view it was a great surprise to see his company link in the footer (moreover he didn't inform me). At that time, I told to myself "well probably this is an industry standard or something". But the bottom line is that I paid for this site and that is why I am not in anyway obliged to advertise the designer who made it.