When the "Save" setting (see MoodleDocs) marked "yes", then this should prevent duplicate certificates. I forget what happens if some certificates have already been issued with
the Save set to "no" and then the setting is changed to "yes".
I suggest creating a new certificate with Save set to "yes" and see if new certificates are given or if the copy of the initially issued certificate comes up.
My certificate version is 2 something. Perhaps this feature of Certificate did not make a seamless transition to 3. Could be broken.
Here is some additional background information about Moodle and at least our 2.x version of Certificate.
The underlying Moodle user id, not the profile name nor username, determines which user participated in an activity (like Certificate). This id is the key unique field in Moodle's database and is never reused. The interface allows changes in other fields but not this one.
In our site, we turn on the Save setting and use the "Print code" feature. Thus user "maven101" who was mistakenly given the profile name of "Kris Koulmen" at the time they received their certificate, will always see it printed that way years later, along with the issued date and unique code. The system administrator can change the user name and the profile name but the certificate will never show the correct user profile name of "Chris Collman".
I believe that the view certificate list will show the corrected profile name of Chris Collman's along with the unique code, but the pdf certificate will say "Kris Koulmen". Changing this certificate is difficult. We warn students to check their profile name before creating their certificate.
Hope this helps. Sorry I was not more specific earlier. If the new test certificate does not work, please give us you version of Moodle and the version of Certificate.