Some instructors would like to create anonymous evaluations, yet be able to record the participants who have taken the survey within Moodle.

Since Moodle takes the anonymous setting literally and does not record the participant's name with the feedback, I created a simple "Choice" (available under "Add an Activity" in Moodle). For the Choice, I simply added, "I have completed the survey" (yes or no).  This only takes a minute to create.

Then, I created a "Feedback" (also available under Add an Activity). Instead of Feedback, you could opt to create an anonymous Questionnaire; they will both work. Once the student completes the survey and clicks the "Submit" button, they receive a thank you page that includes a statement directing the participants to "Please click here to get credit." *This of course is a link to the "Choice" question. The "Feedback" responses are completely anonymous, but the "Choice" records the participant in Moodle. 

*When creating a new feedback (or editing/updating one already created), you will see a text box "After Submitting > Page after submit".  It is within that text box, that I typed, "Thank you! Please click here to get credit for taking the anonymous survey." (You may type whatever you like.)  Then I highlighted the text CLICK HERE and clicked on the "Insert Web link" icon (icon looks like 2 chain links, just to the right of the anchor icon).  When that opens, Click in the URL text box and paste the link to the "Choice" you created. (You can get that link in a variety of ways - If you have any questions on how to get that, just ask the Help Desk).

Anyway, once you have typed/pasted the link into the URL text box, click OK.

Your text should now have an underline.
 
Click the "Save and return to course" button.

That is it!  Now you have the link to the "Choice" available to the student upon submitting their survey responses from your "Feedback".

Later as the Instructor, you are able to click on the "Choices" link and View the responses and know who has taken the survey.

Side note on format & keeping the link to the "Choice" unavailable from the top level:

The above is easiest done in the "Social" format. You may create a link within a Forum that directs your students to the evaluation.

If, however, you are using a "Topic" or "Weekly" format, it would be wise to move the "Choice" to a Topic or Week that is not visible (ex: if you have 10 weeks visible, create an 11th week in the Settings, move the "choice question to the 11th section, and then return the settings to 10 weeks; thus making the choice still live but not readily visible).