You only registered the variable with session_register but you did not set its value. The variable is still empty. The session_register function only registers a variable, it does not set its value, details on the session_register function can be found here: http://www.php.net/manual/en/function.session-register.php
Also since you are using sessions, you do not need to use HTTP_SEESION_VAR to access session variables. Here is an easier way to accomplish your task:
<?php
session_start();
$user = "Daniel";
session_register('user'); //Register a variable called user
$_SESSION['user'] = $user; //Set the session variable user (which was registered above) to the value in the local variable $user
//Add your link to the next page here
?>
<?php
//next page
session_start();
echo $_SESSION['user'];
?>
That should work.
Good luck.