I have the default setup of the Splunk navigation bar where it shows drop-down navigation menus of User Name, Message, Settings, Activity, Help on right side of the bar.
Our client need is to remove all the drop-down navigation menus except for User Name (which allows logout).
What changes do I have to make and where to enable this setup?
You can't without re-writing fundamental pieces that would break things for admin users. One could pull data via API/REST and provide a custom UI via another system, but those menus can't be removed otherwise.
The only way to "change" that bar is with roles, as some roles only display pieces of the Splunkbar. Other than that, don't do this without fully understanding the repercussions of editing core files.