While there is a capability to control hiding the student name and id number when manually grading, this does not hide the students results from the results page:

quiz/grading:viewstudentnames
quiz/grading:viewidnumber

A tutor asks her students to complete quizzes prior to class and would like to anonymise these, to encourage students to complete these without worrying that poor performance will be visible to their tutors. In order to anonymise the results page, the email address would also need to be hidden, along with the name and idnumber.