Recently when designing/creating surveys in Voice Of Customer. I faced this issue of getting anonymous response if I am using email snippet from the survey. Expectation is when you use Email Snippet copied from a survey and put it in an email and send it. Customer fills the survey, you should have the customer/respondent details.
Which means you have to generate survey activities first and copy the direct URL from there and send it but its not what you would want to do every time.
This seems to be a bug in the Voice of Customer Version 188.8.131.52/9.0.1188.4. So please check if you are facing the issue and version is same. Please upgrade it to the latest version. 184.108.40.206/9.0.1438.4.
Doing above resolved my issue and I could see the responses properly.
hope this helps!