This will add a page-slug class and a page-parent-slug class to your body tag, along with all the other defaults. Put this in your functions.php file:
function wpprogrammer_post_name_in_body_class( $classes ){
if( is_singular() ) {
global $post;
$parent = get_page($post->post_parent);
array_push( $classes, "{$post->post_type}-{$post->post_name}" );
array_push( $classes, "{$post->post_type}-parent-{$parent->post_name}" );
}
return $classes;
}
add_filter( 'body_class', 'wpprogrammer_post_name_in_body_class' );
Also make sure your open body tag looks like this (you can probably find it in header.php):
<body <?php body_class(); ?>>
Many thanks to Utkarsh Kuketri for the original function!