Index: wp-includes/author-template.php
===================================================================
--- wp-includes/author-template.php	(revision 42249)
+++ wp-includes/author-template.php	(working copy)
@@ -436,6 +436,10 @@
 
 		if ( $args['show_fullname'] && $author->first_name && $author->last_name ) {
 			$name = "$author->first_name $author->last_name";
+		} else if ( $args['show_fullname'] == false && ! empty( $author->first_name ) ) {
+			$name = "$author->first_name";
+		} else if ( $args['show_fullname'] == false && ! empty( $author->last_name ) ) {
+			$name = "$author->last_name";
 		} else {
 			$name = $author->display_name;
 		}