One of the great features that Moodle allows for is blind grading, where the name of the student submitting the assignment is not known to the instructor. When you create a new assignment in Moodle, one grading option is “Anonymous Submissions,” which you can switch to “Yes” as shown in the screenshot below.
Students are then each assigned a Participant ID number in place of their name. You can choose to “reveal student identities” (see screenshot below), but this would work only after all the assignments have been graded to keep this process blind.
To make sure that the grading remains blind, it is worthwhile to ask students not to include their names in the submitted pdf or Word documents.