diff --git a/core/modules/user/src/Tests/UserRegistrationTest.php b/core/modules/user/src/Tests/UserRegistrationTest.php
index cc5785a..01418b7 100644
--- a/core/modules/user/src/Tests/UserRegistrationTest.php
+++ b/core/modules/user/src/Tests/UserRegistrationTest.php
@@ -7,6 +7,7 @@
 
 namespace Drupal\user\Tests;
 
+use Drupal\Component\Utility\SafeMarkup;
 use Drupal\Core\Field\FieldStorageDefinitionInterface;
 use Drupal\simpletest\WebTestBase;
 
@@ -193,6 +194,24 @@ function testRegistrationDefaultValues() {
   }
 
   /**
+   * Ensures that you cannot register with the same name / mail twice.
+   *
+   * @see \Drupal\user\Plugin\Validation\Constraint\UserNameUnique
+   * @see \Drupal\user\Plugin\Validation\Constraint\UserMailUnique
+   */
+  public function testUniqueFields() {
+    $account = $this->drupalCreateUser([]);
+
+    // Existing username.
+    $this->drupalPostForm('user/register', ['mail' => 'test@example.com', 'name' => $account->getUsername()], t('Create new account'));
+    $this->assertRaw(Safemarkup::format('The username %value is already taken.', ['%value' => $account->getUsername()]));
+
+    // Existing mail address.
+    $this->drupalPostForm('user/register', ['mail' => $account->getEmail(), 'name' => $this->randomString()], t('Create new account'));
+    $this->assertRaw(Safemarkup::format('The email address %value is already taken.', ['%value' => $account->getEmail()]));
+  }
+
+  /**
    * Tests Field API fields on user registration forms.
    */
   function testRegistrationWithUserFields() {
diff --git a/core/modules/user/src/UserAccessControlHandler.php b/core/modules/user/src/UserAccessControlHandler.php
index 4b29b4e..b4bc2b3 100644
--- a/core/modules/user/src/UserAccessControlHandler.php
+++ b/core/modules/user/src/UserAccessControlHandler.php
@@ -81,9 +81,13 @@ protected function checkFieldAccess($operation, FieldDefinitionInterface $field_
     switch ($field_definition->getName()) {
       case 'name':
         // Allow view access to anyone with access to the entity.
-        if ($operation == 'view') {
+        // Anonymous users should be able to change their usernamae
+        if ($operation == 'view' || ($items && $account->isAnonymous() && $items->getEntity()->isAnonymous())) {
           return AccessResult::allowed()->cachePerPermissions();
         }
+        if ($account->isAnonymous()) {
+          return AccessResult::allowed();
+        }
         // Allow edit access for the own user name if the permission is
         // satisfied.
         if ($is_own_account && $account->hasPermission('change own username')) {