If the form element they enter their name is "name", set the message to:
Thank You <?php echo((isset($_POST["name"]))?$_POST["name"]:"") ?>
To hide the form, place an if statement around it:
<?php if(!isset($_GET['sent']) || (isset($_GET['sent']) && $_GET['sent'] != "true")) { ?>
<from...>
......
</from>
<?php } ?>