You should add the following to your functions.php, you can add, edit or delete items to your desire.
remove_action( 'admin_bar_menu', 'wp_admin_bar_wp_menu', 10 );
add_action( 'admin_bar_menu', 'my_admin_bar_wp_menu', 10 );
function my_admin_bar_wp_menu( $wp_admin_bar ) {
$wp_admin_bar->add_menu( array(
'id' => 'wp-logo',
'title' => '<span class="ab-icon"></span>',
'href' => 'http://yourdomain.com',
'meta' => array(
'title' => __('About my website'),
),
) );
if ( is_user_logged_in() ) {
// Add "About WordPress" link
$wp_admin_bar->add_menu( array(
'parent' => 'wp-logo',
'id' => 'about',
'title' => __('About WordPress'),
'href' => self_admin_url( 'about.php' ),
) );
}
// Add WordPress.org link
$wp_admin_bar->add_menu( array(
'parent' => 'wp-logo-external',
'id' => 'wporg',
'title' => __('WordPress.org'),
'href' => __('http://wordpress.org/'),
) );
// Add codex link
$wp_admin_bar->add_menu( array(
'parent' => 'wp-logo-external',
'id' => 'documentation',
'title' => __('Documentation'),
'href' => __('http://codex.wordpress.org/'),
) );
// Add forums link
$wp_admin_bar->add_menu( array(
'parent' => 'wp-logo-external',
'id' => 'support-forums',
'title' => __('Support Forums'),
'href' => __('http://wordpress.org/support/'),
) );
// Add feedback link
$wp_admin_bar->add_menu( array(
'parent' => 'wp-logo-external',
'id' => 'feedback',
'title' => __('Feedback'),
'href' => __('http://wordpress.org/support/forum/requests-and-feedback'),
) );
}
Hope this helps.