You should
<input type="hidden" name="Name"
value="<?php echo htmlentities($_POST['Name'], ENT_QUOTES, 'utf-8'); ?>
Else someone named I_broke_your_html_code_with_double_quote" will screw things up.
And the same applies if you store things in the DB, and then pull it out again for the subsequent forms. You would need to use mysql_real_escape_string or whatever escape function your database and db driver uses.
If those things don't work, what does the code look like for dealing with the name through each form, and what's the user's name?