Hi Heather,
I think this is an option in the Setup area under Tasks & Issues, unless I'm misunderstanding what you're trying to do?
Primary Contact is typically the submitter of the request, though I suppose it is possible to designate someone else if your request queues are set-up that way.
It's also possible to configure it to behave that way for only certain Groups, so it would be possible to be creatively selective about when it would occur if you didn't want it to be a global setting.
Katherine