Hi Matt,
Please don't confuse Username and Nicename. Those are not the same.
Nicenames are used for user @mentioning and in your profile URL. So again, this is the nicename, not username.
If you want to disable the wpDiscuz mentioning feature at all, you should disable the "User Mentioning" option. It's located in the Dashboard > wpDiscuz > Settings > Subscription and User Following admin page.
More info here: https://wpdiscuz.com/docs/wpdiscuz-7/plugin-settings/subscription-and-user-following/#enable-user-mentioning
In any case, if you just want to hide the nicename, but allow people to @menation each other, you should put this code in WordPress active theme functions.php file.
add_filter("wpdiscuz_show_nicename", "__return_false");
This article should be helpful for you: https://www.wpbeginner.com/plugins/how-to-easily-add-custom-code-in-wordpress-without-breaking-your-site/
Important: The code above just hides the nicename next to the display name, but the mentioning feature will be still available if the users know the nicenames of each other.