I figured it out, I think. I found a snippet of code that removed the comment author and then modified it to just manipulate the author’s name. I placed it in my child theme’s functions.php and it did what I wanted it to.
if ( ! function_exists( 'abbreviate_comment_author' ) ) :
function abbreviate_comment_author( $author ){
list($author_first, $author_second) = explode(' ',$author, 2);
$author_second = $author_second[0] . '.';
$author = $author_first . ' ' . $author_second;
return $author;
}
add_filter( 'get_comment_author', 'abbreviate_comment_author' );
add_filter( 'comment_author_rss', 'abbreviate_comment_author' );
endif;