How to remove howdy dropdown menu content

You can use wordpress nodes to customize profile menu.

Add this in functions.php

add_action( 'admin_bar_menu', 'remove_my_account', 999 );
function remove_my_account( $wp_admin_bar ) {
   $wp_admin_bar->remove_node( 'my-account' );
}

add_action( 'admin_bar_menu', 'add_logout', 999 );
function add_logout( $wp_admin_bar ) {
   $args = array(
      'id'     => 'logout',           // id of the existing child node (New > Post)
      'title'  => 'Logout',           // alter the title of existing node
      'parent' => 'top-secondary',    // set parent
  );
  $wp_admin_bar->add_node( $args );
}