Quick answer
Use the “course submissions” report to link a student’s ID with their Turnitin ID.

Full answer
On your Moodle site’s main page, click on the cog wheel (top right), then click "more". Under the "reports" section choose "course submissions". Now select the relevant dropbox and select “Go”. You can now establish whether a student submitted to an anonymous dropbox, and identify a student’s work against their Turnitin submission ID if they failed to use their student number when submitting (use “ctrl-F” to search for a student’s number and identify the Turnitin ID). This means you can still mark anonymously, as all you are using is the student number to locate the work.