instead of changing the name in the cart object file, you can change how it is displayed on the cart display page.
the code that will display the discount name will look like:
<?php echo $YourCart->RuleLooperName("Discounts"); ?>
this will be inside a loop that goes through each discount and displays the name, then the discount amount.
you can display the session in front of the discount name using:
<?php echo($_SESSION['VoucherCode']." ".$YourCart->RuleLooperName("Discounts")); ?>