Using the realname module will lead to the ability to add other realname tokens to the heartbeat template variables. This will end up showing the real names in the stream.
However, for comment, this is not possible this way. I refer to this issue here to show you how that can be altered. Overriding the function theme_heartbeat_comment and implement the code beneath:
<?php
// Change this
$output .= l($account->name, 'user/' . $comment->uid) . ' ';
// Into this
$output .= l(realname_make_name($account), 'user/' . $comment->uid) . ' ';
?>