This way would work … the user_register action is fired when the user is stored in the data base. You can add meta data to a user with add_metadata.
add_action( 'user_register', 'myplugin_registration_save', 10, 1 );
function myplugin_registration_save( $user_id ) {
add_metadata( $user_id, 'unique_number', date( 'Y' ).str_pad( $user_id, 4 ) );
}