In your case $registered is the user id not the user object. So so it does not work. Please changeuse the function code as given below.
add_action( 'user_register', 'set_user_registration_date', 10, 1 ); function set_user_registration_date( $user_id ) { $user = get_userdata ( $user_id ); // Update the registration meta data update_user_meta ( $user_id, 'registration_date', $user->user_registered ); }