Unless this is a greatly simplified version of what you're trying to do, there's no reason to use a form here. You're not posting any data to the form, just using it to get to another page, which technically is what a link is for. It's not a blatantly incorrect use of a form, but it's not really all that --right-- either.
Simply echo the value with a link to the next page. You can style the a:link using something like jQuery buttons or even with an image to mimic a button if that's a requirement.
So, for instance:
<?php
$info = mysql_query ("SELECT * FROM table WHERE name= 'something'");
$info = mysql_fetch_assoc($info));
?>
<html>
<?php echo $info['name']; ?>
<a href="page2.php">Submit</a>
</html>
Another alternative would be do do two stacked divs and show/hide them on click of a button. It requires a little jQuery or javascript, but eliminates the hit to the server in between, making a smoother user experience. It's tough to say what's best without more details of what you're trying to do.
Finally, bear in mind that while sessions do work, there can be issues. For instance, some companies and people turn sessions off (or block them altogether) so they can't be relied on 100%. IE in particular (in some versions) interpreted the user's choice to block cookies to also block sessions. If they have your app open in two tabs, it can get the values confused and result in undesirable outcomes. At the least, it can cause your application to throw all sorts of dialogs that scare users, even though they're really not that big of a deal.