by Andreas Panagiotopoulos.
You have to change the text that is sent to the submission receipt through language customization from the GUI of moodle.
You can visit "SIte Administration" -> "Language" -> "Language customization" and then filter the mod_assign component. The strings you may want is 'submissionreceipthtml', 'submissionreceiptsmall', 'submissionreceipttext'.
There you can edit the text and add more info to it using the placeholder '{a}'.
So, if you want idnumber you can print it with {$a->idnumber}, if you want users email you can print it with {$a->email}.
Of course, you have to check first the function send_assignment_notification in /mod/assign/locallib.php. You may have to add the above variables to info Class.