functions.php

<?php

/**
 * Add Site Name as Body Class
 *
 * @author Bill Erickson
 * @link http://www.billerickson.net/wordpress-class-body-tag/
 *
 * @param array $classes
 * @return array
 */
function be_site_name_in_body( $classes ) {
	$class = str_replace( array( 'http://', 'www.', '.', '/' ), array( '', '', '-', '-' ), home_url() );
	$classes[] = sanitize_html_class( $class );
	return $classes;
}
add_action( 'body_class', 'be_site_name_in_body' );