The following action hooks @ wp-login.php should also pass the user variable:
$message = apply_filters('retrieve_password_message', $message, $key);
-> Also pass $user_login
$user_login is needed to build the URL the user needs to click to confirm the password reset request.
$message = apply_filters('password_reset_message', $message, $new_pass);
-> Also pass $user->user_login
When sending the new password, we need to display the username that goes with it.
(Maybe I missed something...)