Add the snippet below to your themes functions.php file to remove parts of the WordPress admin Header

function remove_admin_bar_links() {
    global $wp_admin_bar;
    $wp_admin_bar->remove_menu('wp-logo'); // Remove the WordPress logo
    $wp_admin_bar->remove_menu('about'); // Remove the about WordPress link
    $wp_admin_bar->remove_menu('wporg'); // Remove the WordPress.org link
    $wp_admin_bar->remove_menu('documentation'); // Remove the WordPress documentation link
    $wp_admin_bar->remove_menu('support-forums'); // Remove the support forums link
    $wp_admin_bar->remove_menu('feedback'); // Remove the feedback link
    $wp_admin_bar->remove_menu('view-site'); // Remove the view site link
    $wp_admin_bar->remove_menu('updates'); // Remove the updates link
    $wp_admin_bar->remove_menu('comments'); // Remove the comments link
    $wp_admin_bar->remove_menu('new-content'); // Remove the content link
}
add_action( 'wp_before_admin_bar_render', 'remove_admin_bar_links' );