TraxOnDaRocks That seems to be more of a governance question. Your idea could work, but if you are managing responses and conducting the analysis, if you reviewed names to make sure that all had completed the survey and then removed them, you might still associate responses with particular individuals, which defeats the purpose of anonymity.
If the intent is to show *what proportion of people in the organization* completed the survey, as opposed to *which individuals* completed the survey, you can track the number of responses against the best number you have for the number of people in the organization, and report that percentage. I would recommend this approach because it shows how successful you were in messaging the survey while preserving anonymity and ensuring that your colleagues are comfortable that their responses will not be associated with them.

Is there some reason why you can't use individual links and email them directly to each employee? If so, you wouldn't have to ask for names up front, and you could enable the Anonymize Responses feature so the data wouldn't link responses to individuals. You would download the Distribution History to see who has and has not responded.