Honoree Information - notify another person
You can't do it without doing some custom work.  The profile is going to create one contact for the honoree, and unfortunately, that's that.  One approach is to have a custom field for the information of who to notify, and then have a report of folks where that's set.  A staff member (who would presumably need to mail things anyway) could check that report and set up a new contact manually.

We have a client who wanted something like this, including automatically sending an email to the other person.  We built a custom extension to do it, and it might be a good starting point for abstracting it into an extension for others.