Display No Network Title In Toolbar

function changes_my_sites($admin_bar) {
	if (current_user_can('manage_network'))

	$admin_bar->add_menu( array(
		'id'    => 'c-network-admin',
		'parent' => 'c-my-sites',
		'title' => 'Network Dashboard',
		'href'  => network_admin_url(),
	));

	$admin_bar->add_menu( array(
		'id'    => 'c-network-sites',
		'parent' => 'c-my-sites',
		'title' => 'Network Sites',
		'href'  => network_admin_url('sites.php'),
	));

	$admin_bar->add_menu( array(
		'id'    => 'c-network-users',
		'parent' => 'c-my-sites',
		'title' => 'Network Users',
		'href'  => network_admin_url('users.php'),
	));

}
add_action('admin_bar_menu', 'changes_my_sites', 20);

Please use above code but change id and title …

Many thanx for your code suggestion. It was the “Network Admin” toolbar menu I was trying to change. So this is what I’m using right now.

//* Disable toolbar site name
add_action( 'wp_before_admin_bar_render', 'disable_site_name' );
function disable_site_name() {
	global $wp_admin_bar;
	if ( is_network_admin() ) {
		$wp_admin_bar->remove_menu( 'site-name' );
	}
}

//* Enable toolbar network title
add_action( 'admin_bar_menu', 'enable_network_title', 30 );
function enable_network_title() {
	global $wp_admin_bar;
	if ( is_network_admin() ) {
		$wp_admin_bar->add_menu( array(
			'id' => 'network-title',
			'title' => __('Network Admin'),
			'href' => network_admin_url(),
		) );
		$wp_admin_bar->add_menu( array(
			'parent' => 'network-title',
			'id' => 'network-sites',
			'title' => __( 'All Sites' ),
			'href' => network_admin_url( 'sites.php' ),
		) );
		$wp_admin_bar->add_menu( array(
			'parent' => 'network-title',
			'id' => 'network-updates',
			'title' => __( 'Updates' ),
			'href' => network_admin_url( 'update-core.php' ),
		) );
		$wp_admin_bar->add_menu( array(
			'parent' => 'network-title',
			'id' => 'network-settings',
			'title' => __( 'Settings' ),
			'href' => network_admin_url( 'settings.php' ),
		) );
	}
}

#wpadminbar #wp-admin-bar-network-title>.ab-item:before {
	content: '\f319';
	font-size: 18px;
	position: relative;
	top: 3px;
}