To use sessions, you need to use session_start(); before using $_SESSION.
...
session_start();
if(isset($_SESSION['name']))
{
echo "<div id='minicart'>";
require_once('include/miniCart.php');
echo "</div>";
}
...
If isset($_SESSION['name'])) returns as false and you don't want anything else to happen, you don't need to set an ELSE within your IF statement.
Let me know how you get on.