$sql_result = "SELECT FirstName FROM $tbl_name WHERE Email='$email' and Password='$mypassword' limit 1";
$res = mysql_query($sql_result);
$value = mysql_fetch_object($res);

$_SESSION['name']=$value['FirstName'];

$_SESSION['name']=$value->FirstName;

$value = mysql_fetch_object($res);
                     ^^^^^^^---- fetching an object

$_SESSION['name']=$value['FirstName'];
                   ^^^^^^^^^---treating it like an array