diff --git a/core/includes/theme.inc b/core/includes/theme.inc
index e8cff8b..62f2d6f 100644
--- a/core/includes/theme.inc
+++ b/core/includes/theme.inc
@@ -1778,7 +1778,7 @@ function drupal_common_theme() {
     ),
     // From menu.inc.
     'menu' => array(
-      'variables' => array('items' => array(), 'attributes' => array()),
+      'variables' => array('menu_name' => NULL, 'items' => array(), 'attributes' => array()),
     ),
     'menu_local_task' => array(
       'render element' => 'element',
diff --git a/core/lib/Drupal/Core/Menu/MenuLinkTree.php b/core/lib/Drupal/Core/Menu/MenuLinkTree.php
index 5b3aee8..3c71930f 100644
--- a/core/lib/Drupal/Core/Menu/MenuLinkTree.php
+++ b/core/lib/Drupal/Core/Menu/MenuLinkTree.php
@@ -177,6 +177,7 @@ public function build(array $tree) {
       // Add the theme wrapper for outer markup.
       // Allow menu-specific theme overrides.
       $build['#theme'] = 'menu__' . strtr($menu_name, '-', '_');
+      $build['#menu_name'] = $menu_name;
       $build['#items'] = $items;
       // Set cache tag.
       $build['#cache']['tags'][] = 'config:system.menu.' . $menu_name;
diff --git a/core/modules/system/tests/src/Unit/Menu/MenuLinkTreeTest.php b/core/modules/system/tests/src/Unit/Menu/MenuLinkTreeTest.php
index ac6af14..d51f6e3 100644
--- a/core/modules/system/tests/src/Unit/Menu/MenuLinkTreeTest.php
+++ b/core/modules/system/tests/src/Unit/Menu/MenuLinkTreeTest.php
@@ -135,6 +135,7 @@ public function providerTestBuildCacheability() {
         'max-age' => Cache::PERMANENT,
       ],
       '#sorted' => TRUE,
+      '#menu_name' => 'mock',
       '#theme' => 'menu__mock',
       '#items' => [
         // To be filled when generating test cases, using $get_built_element().
diff --git a/core/modules/toolbar/src/Menu/ToolbarMenuLinkTree.php b/core/modules/toolbar/src/Menu/ToolbarMenuLinkTree.php
index 6742e6c..d1e22a9 100644
--- a/core/modules/toolbar/src/Menu/ToolbarMenuLinkTree.php
+++ b/core/modules/toolbar/src/Menu/ToolbarMenuLinkTree.php
@@ -30,6 +30,7 @@ public function build(array $tree, $level = 0) {
       $menu_name = $first_link->getMenuName();
       // Add a more specific theme suggestion to differentiate this rendered
       // menu from others.
+      $build['#menu_name'] = $menu_name;
       $build['#theme'] = 'menu__toolbar__' . strtr($menu_name, '-', '_');
       return $build;
     }