There is no way to make it completely anonymous (as in, make it impossible for the Marker to work out who the student is if they really try).
However, you can make it so that the marker can grade without seeing names like this:
- In the quiz settings, go to 'Permissions'.
- There are two permissions which you need to remove from the roles that will be doing the grading:
quiz/grading:viewidnumber
quiz/grading:viewstudentnames
Then when the person doing the grading goes to Quiz settings -> Results -> Manual grading, they won't see names.