If you have a public registration, anyone who receives the link can register, and a new participant will be created for them.
This isn't possible with a closed registration (importing a list and sending invitations). If the individual registration link is forwarded, no new participant is created; instead, access is granted to the existing participant. You can tell this because the participant's login name is still the same as the old one. If the name in the questionnaire is editable, anyone who receives the forwarded invitation can overwrite the name. Therefore, you shouldn't make the participant's name editable in the questionnaire.