Anonymous Marking is a tool in Brightspace which allows you to mark your students Assignment submissions without knowing the identity of the student. Anonymous Marking is only available for Assignments. In general, Anonymous Marking anonymizes the submitted work.
As you can see at number 1, the students will all be shown as Anonymous User, but the activity name will be visible (in this case the Assignment is called AnonymousTest).
If you click on Anonymous User, you see the evaluation page. Here you can give feedback to your students (1), but as you can see, you are not able to publish this feedback (2). To publish feedback on anonymous assignments, you have to go to Assignments > Select your assignment (in this case AnonymousTest) > Publish All Feedback.
Anonymous Marking can be used in combination with Turnitin. When Grademark is opened from Turnitin, the students name will not be displayed and set to 'Anonymous'.