diff --git a/wp-includes/ms-load.php b/wp-includes/ms-load.php
index 6adbac35a8..02224bd548 100644
--- a/wp-includes/ms-load.php
+++ b/wp-includes/ms-load.php
@@ -426,13 +426,13 @@ function ms_not_installed() {
  *
  * @access private
  * @since 3.0.0
- * @deprecated 3.9.0
+ * @deprecated 3.9.0 Use get_current_site() instead.
  *
  * @param object $current_site
  * @return object
  */
 function get_current_site_name( $current_site ) {
-	_deprecated_function( __FUNCTION__, '3.9' );
+	_deprecated_function( __FUNCTION__, '3.9', 'get_current_site()' );
 	return $current_site;
 }