Aaron Axelsen

Overrides the <code>wp_notify_moderator</code> function located in pluggable.php. By default, wordpress does not notify a comment author of a moderation 
event. This plugin will look at all users in the blog, and notify anyone who can moderate the plugin, along with the admins and the author 
of that post. This has been tested and does work with WPMU as well.

Post Author Comment Notification

Overrides the wp_notify_moderator function located in pluggable.php.  By default, wordpress does not notify a comment author of a moderation

Sparanoid

Displays a user badge next to the comment author name based on author’s role.
<ul>
<li>No database writes, no configurations, install, activate and go.</li>
<li>Easy styles customization via Jetpack Custom CSS or built-in Custom CSS (WordPress version 4.7 or higher required).</li>
<li>Works with <a href="https://wordpress.org/plugins/current-theme-body-class/" rel="ugc">Current Theme Body Class</a> plugin.</li>
</ul>

Comment Author Role Badge

Displays a user badge next to the comment author name based on author's role.

Post Author Comment Notification vs Comment Author Role Badge