Please see the below 2 scripts to remove the howdy in Wordpress, you can use any 1:

Solution 1:

add_filter( 'admin_bar_menu', 'replace_wordpress_howdy', PHP_INT_MAX - 100);
function replace_wordpress_howdy( $wp_admin_bar ) {
	$my_account = $wp_admin_bar->get_node('my-account');
	$wp_admin_bar->add_node( array(
	'id' => 'my-account',
	'title' => substr($my_account->title, strpos($my_account->title, '<span class="display-name">')),
	));
}

Solution 2:

function pac_da_custom_admin_bar_user_name() {
    global $wp_admin_bar;
    // Define the ID of the node representing the "My Account" section in the admin bar.
    $node_id = 'my-account';
    // Check if the specified node exists in the admin bar.
    if ($wp_admin_bar->get_node($node_id)) {
        // Get the current title of the "My Account" section.
        $current_title = $wp_admin_bar->get_node($node_id)->title;
        // Split the current title into an array based on the comma and space separator.
        $newTitle = explode(", ", $current_title);
        // Update the "My Account" section title with the second part of the split title if available, 
        // otherwise keep the current title.
        $wp_admin_bar->add_node(array(
            'id' => $node_id,
            'title' => isset($newTitle) && isset($newTitle[1]) ? $newTitle[1] : $current_title,
        ));
    }
}
// Hook the custom admin bar user name function to run before the admin bar is rendered.
add_action('wp_before_admin_bar_render', 'pac_da_custom_admin_bar_user_name');