by Andreas Panagiotopoulos.
Using moodle 2.5, you can edit function download_submissions() in mod/assign/locallib.php file.
There, at line 2300, you can change this statement $prefix = clean_filename($prefix . '_' . $this->get_uniqueid_for_user($userid) . '_') in order to add student id (or idnumber) like this " .$student->id" .
So, you can edit that line with the this: $prefix = clean_filename($prefix . '_' . .$student->id . '_'); to have user id.
Is this a solution for you?