That's what we do in our zendesk. we hide the subject field and populate it at the point of submitting with values the user entered into other fields. This example creates a subject like "New User John Doe 2019-01-01"

So in addition to hiding the fields like Dan does, we add this code that sets the subject field upon submitting the ticket.

$("#new_request").submit(function(e){

//33860927 = FirstName
//33855548 = LastName
//33855528 = FirstDayOfWork

var subject_value = "New User " + $("#request_custom_fields_33860927").val() + " " + $("#request_custom_fields_33855548").val() + " " + $("#request_custom_fields_33855528").val();

$('#request_subject').val(subject_value);

});