The same way you would in any other PHP program:
header("HTTP/1.1 401 Unauthorized");
exit;
WordPress has special handling for 404 because there’s a 404 template. Usually if something happens such as a 401, there is no special template, but you can make use of wp_die
which will show a message in a simple UI
header("HTTP/1.1 401 Unauthorized");
wp_die( 'forbidden' );
This will show the message in a white rectangle with rounded edges and sans-serif text on a gray background, then call exit
/die