If a non-personalized link is used, SoSci Survey has no means to identify who the person is that does the survey.
another way to get around this other than sending personalized emails?
Depends on what your design looks like. But in general, you either identify the respondents or you do not. And if you don't, then you will not know who already did the survey.
SoSci Survey also provides a compromise, which is a privacy mode for email addresses that will anonymize the data after the survey has been finished. But this still required personalized links.