Change "Site Name" menu in WordPress administration menu bar

functions.admin_bar_menu.site_name_menu.php

<?php

/**
 * code to be placed in theme functions.php
 * Default behavior is to ellipse $blogname at 40 characters.
 * add_filter priority of 30 or greater.
 */
if ( ! function_exists( 'mytheme_admin_bar_menu' ) ) {
	function mytheme_admin_bar_menu( $wp_admin_bar ) {
		$site_name = (object) $wp_admin_bar->get_node( 'site-name' );
		if ( ! empty( $site_name->title ) ) {
			$site_name->title = 'My Site';
			$wp_admin_bar->add_node( $site_name );
		}
	}

	add_filter( 'admin_bar_menu', 'mytheme_admin_bar_menu', 30 );
}