if you look carefully at the confirm page, you will see that for every form element on the checkout page, there is code to store the value from the checkout page into a session variable near the top of the page, and there is a hidden form element to re send that value near the bottom of the page.
on your confirm page, look for the section of code that stores the session variables, and add this:
<?php
if (!session_id()) session_start();
if($_SERVER["REQUEST_METHOD"] == "POST") {
$_SESSION["companyname"] = "".((isset($_POST["companyname"]))?$_POST["companyname"]:"") ."";
}
?>
then find the collection of hidden form elements and add this:
<input type="hidden" name="firstname" id="firstname" value="<?php echo ((isset($_SESSION["companyname"]))?$_SESSION["companyname"]:"") ?>" />