User names are already displayed by default as long as you are logged in.
The option to whether or not display usernames you are referring it's for non-registered users only.
The system cannot guess what's the name of the person who's asking the question by magic, that's why that option exists. So unregistered users can display personalized names other than Anonymous.
If you want to always display usernames every time someone asks a question, just edit the privileges of asking a question in the Admin Panel, for Logged-in users only.
Admin > Permissions > Asking Questions
(You might want to do this for answers as well)
This way a username will always be displayed.