diff --git a/core/includes/update.inc b/core/includes/update.inc
index 5556690..e395fb6 100644
--- a/core/includes/update.inc
+++ b/core/includes/update.inc
@@ -239,7 +239,7 @@ function update_invoke_post_update($function, &$context) {
       $key_value_store = \Drupal::keyValue('update__post_update');
       $executed_updates = $key_value_store->get('existing_updates', []);
       $executed_updates[] = $function;
-      $key_value_store->set($module, $executed_updates);
+      $key_value_store->set('existing_updates', $executed_updates);
     }
       // @TODO We may want to do different error handling for different
       // exception types, but for now we'll just log the exception and
diff --git a/core/lib/Drupal/Core/Extension/module.api.php b/core/lib/Drupal/Core/Extension/module.api.php
index b4b0cf8..8dc2e40 100644
--- a/core/lib/Drupal/Core/Extension/module.api.php
+++ b/core/lib/Drupal/Core/Extension/module.api.php
@@ -662,10 +662,12 @@ function hook_update_N(&$sandbox) {
 /**
  * Executes an update which is intended to update data, like entities.
  *
+ * These implementations have to be placed in a $module.post_update.php file.
+ *
  * These updates are executed after all hook_update_N() implementations. At this
  * stage Drupal is already fully repaired so you can use any API as you wish.
  *
- * Note: In contrast to hook_update_N there is no enforced order, so you can
+ * Note: In contrast to hook_update_N() there is no enforced order, so you can
  * also use machine names for the name of those updates.
  *
  * @param array $sandbox
@@ -678,8 +680,8 @@ function hook_update_N(&$sandbox) {
  *   PDOException.
  *
  * @return string|null
- *   Optionally, update hooks may return a translated string that will be
- *   displayed to the user after the update has completed. If no message is
+ *   Optionally, post_update_Name hooks may return a translated string that will
+ *   be displayed to the user after the update has completed. If no message is
  *   returned, no message will be presented to the user.
  *
  * @ingroup update_api
diff --git a/core/modules/system/src/Controller/DbUpdateController.php b/core/modules/system/src/Controller/DbUpdateController.php
index 043e61d..5aac272 100644
--- a/core/modules/system/src/Controller/DbUpdateController.php
+++ b/core/modules/system/src/Controller/DbUpdateController.php
@@ -259,6 +259,7 @@ protected function selection(Request $request) {
     $build['start']['system'] = array();
 
     $starting_updates = array();
+    $incompatible_updates_exist = FALSE;
     foreach (['update', 'post_update'] as $update_type) {
       switch ($update_type) {
         case 'update':
@@ -269,7 +270,6 @@ protected function selection(Request $request) {
           $updates = $after_update_registry->getMissingUpdateList();
           break;
       }
-      $incompatible_updates_exist = FALSE;
       foreach ($updates as $module => $update) {
         if (!isset($update['start'])) {
           $build['start'][$module] = array(
@@ -601,7 +601,6 @@ protected function triggerBatch(Request $request) {
       }
     }
 
-
     $batch['operations'] = $operations;
     $batch += array(
       'title' => $this->t('Updating'),
diff --git a/core/modules/system/src/Tests/Update/UpdatePostUpdateTest.php b/core/modules/system/src/Tests/Update/UpdatePostUpdateTest.php
index 8be271f..2dd1fbd 100644
--- a/core/modules/system/src/Tests/Update/UpdatePostUpdateTest.php
+++ b/core/modules/system/src/Tests/Update/UpdatePostUpdateTest.php
@@ -20,18 +20,21 @@ class UpdatePostUpdateTest extends UpdatePathTestBase {
   protected function setDatabaseDumpFiles() {
     $this->databaseDumpFiles = [
       __DIR__ . '/../../../tests/fixtures/update/drupal-8.bare.standard.php.gz',
-      __DIR__ . '/../../../tests/fixtures/update/drupal-8.update-test-post-update-enabled.php',
+      __DIR__ . '/../../../tests/fixtures/update/drupal-8.update-test-postupdate-enabled.php',
     ];
   }
 
-  public function testUpdateAfter() {
+  /**
+   * Tests hook_post_update_NAME().
+   */
+  public function testPostUpdate() {
     $this->runUpdates();
 
     $updates = [
-      'update_test_post_update_post_update_first',
-      'update_test_post_update_post_update_second',
-      'update_test_post_update_post_update_test1',
-      'update_test_post_update_post_update_test0',
+      'update_test_postupdate_post_update_first',
+      'update_test_postupdate_post_update_second',
+      'update_test_postupdate_post_update_test1',
+      'update_test_postupdate_post_update_test0',
     ];
     $this->assertIdentical($updates, \Drupal::state()->get('post_update_test_execution', []));
 
diff --git a/core/modules/system/tests/fixtures/update/drupal-8.update-test-post-update-enabled.php b/core/modules/system/tests/fixtures/update/drupal-8.update-test-postupdate-enabled.php
similarity index 84%
rename from core/modules/system/tests/fixtures/update/drupal-8.update-test-post-update-enabled.php
rename to core/modules/system/tests/fixtures/update/drupal-8.update-test-postupdate-enabled.php
index 3d5af10..1b2d186 100644
--- a/core/modules/system/tests/fixtures/update/drupal-8.update-test-post-update-enabled.php
+++ b/core/modules/system/tests/fixtures/update/drupal-8.update-test-postupdate-enabled.php
@@ -12,10 +12,10 @@
 // Set the schema version.
 $connection->merge('key_value')
   ->condition('collection', 'system.schema')
-  ->condition('name', 'update_test_post_update')
+  ->condition('name', 'update_test_postupdate')
   ->fields([
     'collection' => 'system.schema',
-    'name' => 'update_test_post_update',
+    'name' => 'update_test_postupdate',
     'value' => 'i:8000;',
   ])
   ->execute();
@@ -28,7 +28,7 @@
   ->execute()
   ->fetchField();
 $extensions = unserialize($extensions);
-$extensions['module']['update_test_post_update'] = 8000;
+$extensions['module']['update_test_postupdate'] = 8000;
 $connection->update('config')
   ->fields([
     'data' => serialize($extensions),
diff --git a/core/modules/system/tests/modules/update_test_post_update/update_test_post_update.info.yml b/core/modules/system/tests/modules/update_test_postupdate/update_test_postupdate.info.yml
similarity index 100%
rename from core/modules/system/tests/modules/update_test_post_update/update_test_post_update.info.yml
rename to core/modules/system/tests/modules/update_test_postupdate/update_test_postupdate.info.yml
diff --git a/core/modules/system/tests/modules/update_test_post_update/update_test_post_update.post_update.php b/core/modules/system/tests/modules/update_test_postupdate/update_test_postupdate.post_update.php
similarity index 78%
rename from core/modules/system/tests/modules/update_test_post_update/update_test_post_update.post_update.php
rename to core/modules/system/tests/modules/update_test_postupdate/update_test_postupdate.post_update.php
index 7ff4945..d67ea14 100644
--- a/core/modules/system/tests/modules/update_test_post_update/update_test_post_update.post_update.php
+++ b/core/modules/system/tests/modules/update_test_postupdate/update_test_postupdate.post_update.php
@@ -3,7 +3,7 @@
 /**
  * First update.
  */
-function update_test_post_update_post_update_first() {
+function update_test_postupdate_post_update_first() {
   $execution = \Drupal::state()->get('post_update_test_execution', []);
   $execution[] = __FUNCTION__;
   \Drupal::state()->set('post_update_test_execution', $execution);
@@ -12,7 +12,7 @@ function update_test_post_update_post_update_first() {
 /**
  * Second update.
  */
-function update_test_post_update_post_update_second() {
+function update_test_postupdate_post_update_second() {
   $execution = \Drupal::state()->get('post_update_test_execution', []);
   $execution[] = __FUNCTION__;
   \Drupal::state()->set('post_update_test_execution', $execution);
@@ -21,7 +21,7 @@ function update_test_post_update_post_update_second() {
 /**
  * Test1 update.
  */
-function update_test_post_update_post_update_test1() {
+function update_test_postupdate_post_update_test1() {
   $execution = \Drupal::state()->get('post_update_test_execution', []);
   $execution[] = __FUNCTION__;
   \Drupal::state()->set('post_update_test_execution', $execution);
@@ -30,7 +30,7 @@ function update_test_post_update_post_update_test1() {
 /**
  * Test2 update.
  */
-function update_test_post_update_post_update_test0() {
+function update_test_postupdate_post_update_test0() {
   $execution = \Drupal::state()->get('post_update_test_execution', []);
   $execution[] = __FUNCTION__;
   \Drupal::state()->set('post_update_test_execution', $execution);
diff --git a/core/tests/Drupal/Tests/Core/Update/UpdateRegistryTest.php b/core/tests/Drupal/Tests/Core/Update/UpdateRegistryTest.php
index e90acaa..e1d69c2 100644
--- a/core/tests/Drupal/Tests/Core/Update/UpdateRegistryTest.php
+++ b/core/tests/Drupal/Tests/Core/Update/UpdateRegistryTest.php
@@ -101,7 +101,7 @@ public function testGetMissingUpdateFunctionsWithNoExistingUpdates() {
     $this->setupBasicModules();
 
     $key_value = $this->prophesize(KeyValueStoreInterface::class);
-    $key_value->get('core.update__post_update', [])->willReturn([]);
+    $key_value->get('existing_updates', [])->willReturn([]);
     $key_value = $key_value->reveal();
 
     $update_registry = new UpdateRegistry('vfs://drupal', 'sites/default', [
@@ -123,7 +123,7 @@ public function testGetMissingUpdateFunctionsWithExistingUpdates() {
     $this->setupBasicModules();
 
     $key_value = $this->prophesize(KeyValueStoreInterface::class);
-    $key_value->get('core.update__post_update', [])->willReturn(['module_a_post_update_a']);
+    $key_value->get('existing_updates', [])->willReturn(['module_a_post_update_a']);
     $key_value = $key_value->reveal();
 
     $update_registry = new UpdateRegistry('vfs://drupal', 'sites/default', [
@@ -145,7 +145,7 @@ public function testGetMissingUpdateList() {
     $this->setupBasicModules();
 
     $key_value = $this->prophesize(KeyValueStoreInterface::class);
-    $key_value->get('core.update__post_update', [])->willReturn([]);
+    $key_value->get('existing_updates', [])->willReturn([]);
     $key_value = $key_value->reveal();
 
     $update_registry = new UpdateRegistry('vfs://drupal', 'sites/default', [
@@ -170,7 +170,7 @@ public function testGetMissingUpdateListWithExistingUpdates() {
     $this->setupBasicModules();
 
     $key_value = $this->prophesize(KeyValueStoreInterface::class);
-    $key_value->get('core.update__post_update', [])->willReturn(['module_a_post_update_a']);
+    $key_value->get('existing_updates', [])->willReturn(['module_a_post_update_a']);
     $key_value = $key_value->reveal();
 
     $update_registry = new UpdateRegistry('vfs://drupal', 'sites/default', [