I am having the same issue, because my quizzes get reported to an entity upon completion. Right now, I do this manually, but I am having an API built, and I will have to restrict reprints of certificates inside the logic of the API. Also, in site administration > plugins > authentication > manage authentication, I will set my authentication settings to lock the name so they cannot change that, and perhaps alter the system and reprint certificates for their friends. Maybe this is useless, as the API will likely use the user's id assigned in the database, but I am just a step above a novice learning this stuff by trial and error.
I hope this helps...I have no suggestion for doing this within Moodle.