Adjusting the admin toolbar menu
The followings are some adjustments one can make with the top admin toolbar menu.
The codex has some pretty good resources for this:
WordPress Core trac ticket:
Core project being worked on here: https://github.com/helen/wp-toolbar-experiments
The mission to make the top admin toolbar more useful.
Inspect element to find the id
To adjust a menu item one has to first find the correct id (node) of the link.
Right click the menu link in your browser and select Inspect Element (name will vary from browser to browser) to open the panel to where one can see the html and css of the page you are on.
Notice the id tag.
I am looking at adjusting the sites drop down. So I will find the id: wp-admin-bar-site-name.
To find the correct node one has to remove: wp-admin-bar-. What is left is the site-name.
The various top level and submenu nodes in the admin toolbar are:
Inside the root-default we have:
top-secondary (The Howdy, name part on the right)
user-actions (beside your avatar image)
Removing a top level node removes the link and submenu if it has one.
If your using the code in the beginning of your functions.php file then include the <?php before the below code.
Example 1. Adding a node (sub menu link) to the site name menu.
Example 2. Adding two nodes to the site name menu.
Example 3. Adding a top level node I named Custom Made having it link to an external web site. Adding two nodes (sub menu links) to the Custom Made menu.
Example 4. Removing all customizer links. Adding multiple nodes (sub menu links) Media Library, Plugins, Themes, All Pages, All Posts to the site name menu.
Example 5. Remove the admin toolbar.
I might add on to this article with other adjustments that can be done with the admin toolbar.
A few Admin Toolbar plugins:
Other helpful resources that also have additional customizations of the admin toolbar:
Do it with wp.com: customize WordPress admin bar
heera.it: customize admin menu bar in WordPress
The first answer to the question was helpful in adjusting the code.
stackoverflow.com: questions WordPress admin bar not displaying both custom drop down menus
digwp.com: admin bar tricks
A special thank you to Drew for helping me with the code.