I am not sure if there is any way to do this on the front-end of Canvas as a user. I'm not sure if there is any way to do this on the back end, either. This sounds like something you might want to submit as a Feature Idea here in the Community. However, since you appear to be a "New Member", your ranking may not yet allow you to submit a new Feature Idea until you've participated more int he Community. See Welcome New Members - Instructure Community (canvaslms.com) and the links in Kristin's blog post.
The Feature Idea links I typically give to people are:
Even though this isn't a great answer to your question, I hope these links will be of some help to you.
What student Id or number are you talking about? The Canvas id for the student is included in the download. All of my bulkdownloads are in the following format:
Where studentName is the students lastNamefirstName (all run together like doejohn),
12345 is the students canvas id and 123456789 is I am assuming the canvas file id for their submission
and of course assignmentName is whatever the name the student used for their assignment.
the canvas id is unique to a student. if that is not the id you want, you should be able to easily create a table matching a canvas id to a student id. At my institution, when I export the gradebook, I have a column for the canvas id and one for the students school id number(maybe this is the number you want). I could easily from that download leave those 2 columns in a spread sheet to have that lookup.
if it is indeed the schools student id that you want(and you don't see it in the gradebook export) then you should be able to get your administrators to add that field into the gradebook as a hidden field that comes with the export.