I used some code from another post...
$('input[type=file]').val()
..and added the ID of each specific file input field. The code below gets the path from the input, pulls only the filename from it and shows that value in a different field for two different file upload fields. If you had a ton of them, you could create a loop based on this code:
$('#File1').change(function(){ // when you leave the File1 form field
var filename1 = $('input[type=file][id=File1]').val().split('\\').pop(); // get just the filename
$('#DL_Filename1').val(filename1); // and place it in the DL_Filename1 box
}); // end change
$('#File2').change(function(){ // when you leave the File2 form field
var filename2 = $('input[type=file][id=File2]').val().split('\\').pop(); // get just the filename
$('#DL_Filename2').val(filename2); // and place it in the DL_Filename2 box
}); // end change