Hi!
I would consider this a bug. It is not difficult to fix, see the file components/com_jcomments/tpl/default/tpl_email.php between line 42 and 46 (in version 2.2.0.2):
<a style="color: #3c452d;font: bold 1em Verdana, Arial, Sans-Serif;" href="<?php echo $comment->homepage; ?>" target="_blank"><?php echo $comment->name; ?></a>
<?php
} else {
?>
<span style="color: #3c452d;font: bold 1em Verdana, Arial, Sans-Serif;"><?php echo $comment->name; ?></span>
You can hardcode the other behaviour (always displaying the username) by changing $comment->name to $comment->username (at both occurences).
It would be better to use a conditional statement, but I do not have time to find out how to read the display_author setting the "correct" way. The above mentioned workaround suits me fine (for now, at least).