diff --git a/core/modules/media/src/Entity/Media.php b/core/modules/media/src/Entity/Media.php
index 49f7283..dc8e0dc 100644
--- a/core/modules/media/src/Entity/Media.php
+++ b/core/modules/media/src/Entity/Media.php
@@ -404,12 +404,7 @@ public static function baseFieldDefinitions(EntityTypeInterface $entity_type) {
         'weight' => -5,
       ])
       ->setDisplayConfigurable('form', TRUE)
-      ->setDisplayConfigurable('view', TRUE)
-      ->setDisplayOptions('view', [
-        'label' => 'hidden',
-        'type' => 'string',
-        'weight' => -5,
-      ]);
+      ->setDisplayConfigurable('view', TRUE);
 
     $fields['thumbnail'] = BaseFieldDefinition::create('image')
       ->setLabel(t('Thumbnail'))
diff --git a/core/modules/media/templates/media.html.twig b/core/modules/media/templates/media.html.twig
index 4173199..32cdb0f 100644
--- a/core/modules/media/templates/media.html.twig
+++ b/core/modules/media/templates/media.html.twig
@@ -32,17 +32,6 @@
  */
 #}
 <div{{ attributes }}>
-  {#
-    In the 'full' view mode the entity label is assumed to be displayed as the
-    page title, so we do not display it here.
-  #}
-  {{ title_prefix }}
-  {% if label and view_mode != 'full' %}
-    <h2{{ title_attributes }}>
-      {{ label }}
-    </h2>
-  {% endif %}
   {{ title_suffix }}
-
   {{ content }}
 </div>
diff --git a/core/modules/media/tests/src/Functional/MediaContextualLinksTest.php b/core/modules/media/tests/src/Functional/MediaContextualLinksTest.php
new file mode 100644
index 0000000..1d97773
--- /dev/null
+++ b/core/modules/media/tests/src/Functional/MediaContextualLinksTest.php
@@ -0,0 +1,45 @@
+<?php
+
+namespace Drupal\Tests\media\Functional;
+
+use Drupal\media\Entity\Media;
+
+/**
+ * Tests views contextual links on media items.
+ *
+ * @group media
+ */
+class MediaContextualLinksTest extends MediaFunctionalTestBase {
+
+  /**
+   * {@inheritdoc}
+   */
+  public static $modules = [
+    'contextual',
+  ];
+
+  /**
+   * Tests contextual links.
+   */
+  public function testMediaContextualLinks() {
+    // Create a media type.
+    $mediaType = $this->createMediaType();
+
+    // Create a media item.
+    $media = Media::create([
+      'bundle' => $mediaType->id(),
+      'name' => 'Unnamed',
+    ]);
+    $media->save();
+
+    $user = $this->drupalCreateUser([
+      'administer media',
+      'access contextual links',
+    ]);
+    $this->drupalLogin($user);
+
+    $this->drupalGet('media/' . $media->id());
+    $this->assertSession()->elementAttributeContains('css', 'div[data-contextual-id]', 'data-contextual-id', 'media:media=' . $media->id() . ':');
+  }
+
+}
diff --git a/core/modules/media/tests/src/FunctionalJavascript/MediaDisplayTest.php b/core/modules/media/tests/src/FunctionalJavascript/MediaDisplayTest.php
new file mode 100644
index 0000000..5282270
--- /dev/null
+++ b/core/modules/media/tests/src/FunctionalJavascript/MediaDisplayTest.php
@@ -0,0 +1,172 @@
+<?php
+
+namespace Drupal\Tests\media\FunctionalJavascript;
+
+use Drupal\Core\Config\FileStorage;
+use Drupal\Core\Config\InstallStorage;
+use Drupal\Core\Config\StorageInterface;
+use Drupal\Core\Entity\Entity\EntityViewDisplay;
+use Drupal\field\Entity\FieldConfig;
+use Drupal\field\Entity\FieldStorageConfig;
+use Drupal\media\Entity\Media;
+use Drupal\node\Entity\Node;
+use Drupal\node\Entity\NodeType;
+
+/**
+ * Basic display tests for Media.
+ *
+ * @group media
+ */
+class MediaDisplayTest extends MediaJavascriptTestBase {
+
+  /**
+   * {@inheritdoc}
+   */
+  protected function setUp() {
+    parent::setUp();
+
+    // Instal the optional configs from the standard profile.
+    $extension_path = drupal_get_path('profile', 'standard');
+    $optional_install_path = $extension_path . '/' . InstallStorage::CONFIG_OPTIONAL_DIRECTORY;
+    $storage = new FileStorage($optional_install_path);
+    $this->container->get('config.installer')->installOptionalConfig($storage, '');
+    // Reset all the static caches and list caches.
+    $this->container->get('config.factory')->reset();
+  }
+
+  /**
+   * Test basic media display.
+   */
+  public function testMediaDisplay() {
+    $assert_session = $this->assertSession();
+    $page = $this->getSession()->getPage();
+
+    $media_type = $this->createMediaType();
+
+    // Create a media item.
+    $media = Media::create([
+      'bundle' => $media_type->id(),
+      'name' => 'Fantastic!',
+    ]);
+    $media->save();
+
+    $this->drupalGet('media/' . $media->id());
+    // Verify the "name" field is really not present.
+    $assert_session->elementNotExists('css', '.field--name-name');
+
+    // Enable the field on the display and verify it becomes visible on the UI.
+    $this->drupalGet("/admin/structure/media/manage/{$media_type->id()}/display");
+    $page->selectFieldOption('fields[name][region]', 'content');
+    $assert_session->waitForElementVisible('css', '#edit-fields-name-settings-edit');
+    $page->pressButton('Save');
+    $this->drupalGet('media/' . $media->id());
+    // Verify the name is present, and its text matches what is expected.
+    $assert_session->elementExists('css', '.field--name-name');
+    $name_field = $page->find('css', '.field--name-name .field__item');
+    $this->assertEquals($media->label(), $name_field->getText());
+
+    // In the standard profile, there are some pre-cooked types. Make sure the
+    // elements configured on their displays are the expected ones.
+    $this->drupalGet('media/add/image');
+    $image_media_name = 'Fantastic image asset!';
+    $page->fillField('name[0][value]', $image_media_name);
+    $page->attachFileToField('files[field_media_image_0]', \Drupal::root() . '/core/modules/media/tests/fixtures/example_1.jpeg');
+    $result = $assert_session->waitForButton('Remove');
+    $this->assertNotEmpty($result);
+    $page->fillField('field_media_image[0][alt]', 'Image Alt Text 1');
+    $page->pressButton('Save');
+    $image_media_id = $this->container->get('entity.query')->get('media')
+      ->sort('mid', 'DESC')
+      ->execute();
+    $image_media_id = reset($image_media_id);
+
+    // Here we expect to see only the image, nothing else.
+    // 1) Assert only one element in the content region.
+    $this->assertEquals(1, count($page->findAll('css', '.media--type-image > div')));
+    // 2) Assert the image is present inside the media element, with "medium"
+    // image style.
+    $media_item = $assert_session->elementExists('css', '.media--type-image > div');
+    $assert_session->elementExists('css', 'img.image-style-medium', $media_item);
+
+    $test_filename = $this->randomMachineName() . '.txt';
+    $test_filepath = 'public://' . $test_filename;
+    file_put_contents($test_filepath, $this->randomMachineName());
+    $this->drupalGet("media/add/file");
+    $page->fillField('name[0][value]', 'File media 1');
+    $page->attachFileToField("files[field_media_file_0]", \Drupal::service('file_system')->realpath($test_filepath));
+    $result = $assert_session->waitForButton('Remove');
+    $this->assertNotEmpty($result);
+    $page->pressButton('Save');
+
+    // Here we expect to see only the linked filename.
+    // 1) Assert only one element in the content region.
+    $this->assertEquals(1, count($page->findAll('css', 'article.media--type-file > div')));
+    // 2) Assert the file link is present, and its text matches the filename.
+    $assert_session->elementExists('css', 'article.media--type-file .field--name-field-media-file a');
+    $link = $page->find('css', 'article.media--type-file .field--name-field-media-file a');
+    $this->assertEquals($test_filename, $link->getText());
+
+    // Create a node type "page" to use as host entity.
+    $node_type = NodeType::create([
+      'type' => 'page',
+      'name' => 'Page',
+    ]);
+    $node_type->save();
+
+    // Reference the created media using an entity_refernce field and make sure
+    // the output is what we expect.
+    $storage = FieldStorageConfig::create([
+      'entity_type' => 'node',
+      'field_name' => 'field_related_media',
+      'type' => 'entity_reference',
+      'settings' => [
+        'target_type' => 'media',
+      ],
+    ]);
+    $storage->save();
+
+    FieldConfig::create([
+      'field_storage' => $storage,
+      'entity_type' => 'node',
+      'bundle' => $node_type->id(),
+      'label' => 'Related media',
+      'settings' => [
+        'handler_settings' => [
+          'target_bundles' => [
+            'image' => 'image',
+          ],
+        ],
+      ],
+    ])->save();
+
+    entity_get_display('node', $node_type->id(), 'default')
+      ->setComponent('field_related_media', [
+        'type' => 'entity_reference_entity_view',
+        'label' => 'hidden',
+        'settings' => [
+          'view_mode' => 'full',
+        ],
+      ])->save();
+
+    $node = Node::create([
+      'title' => 'Host node',
+      'type' => $node_type->id(),
+      'field_related_media' => [
+        'target_id' => $image_media_id,
+      ],
+    ]);
+    $node->save();
+
+    $this->drupalGet('/node/' . $node->id());
+    // Media field is there.
+    $assert_session->elementExists('css', '.field--name-field-related-media');
+    // Media name element is not there.
+    $assert_session->elementNotExists('css', '.field--name-name');
+    $assert_session->pageTextNotContains($image_media_name);
+    // Only one element is present inside the media container.
+    $this->assertEquals(1, count($page->findAll('css', '.field--name-field-related-media article.media--type-image > div')));
+    // Assert the image is present, with "medium" image style.
+    $assert_session->elementExists('css', '.field--name-field-related-media article.media--type-image img.image-style-medium');
+  }
+
+}
diff --git a/core/modules/media/tests/src/Kernel/MediaTest.php b/core/modules/media/tests/src/Kernel/MediaTest.php
index d246fb6..df48a9b 100644
--- a/core/modules/media/tests/src/Kernel/MediaTest.php
+++ b/core/modules/media/tests/src/Kernel/MediaTest.php
@@ -21,14 +21,17 @@ public function testEntity() {
   }
 
   /**
-   * Ensure media name is configurable on manage display.
+   * Tests the Media "name" base field behavior.
    */
-  public function testNameIsConfigurable() {
+  public function testNameBaseField() {
     /** @var \Drupal\Core\Field\BaseFieldDefinition[] $field_definitions */
     $field_definitions = $this->container->get('entity_field.manager')
       ->getBaseFieldDefinitions('media');
 
+    // Ensure media name is configurable on manage display.
     $this->assertTrue($field_definitions['name']->isDisplayConfigurable('view'));
+    // Ensure it is not visible by default.
+    $this->assertEquals($field_definitions['name']->getDisplayOptions('view'), ['region' => 'hidden']);
   }
 
 }
diff --git a/core/profiles/standard/config/optional/core.entity_view_display.media.file.default.yml b/core/profiles/standard/config/optional/core.entity_view_display.media.file.default.yml
index f42bab7..72b0bdc 100644
--- a/core/profiles/standard/config/optional/core.entity_view_display.media.file.default.yml
+++ b/core/profiles/standard/config/optional/core.entity_view_display.media.file.default.yml
@@ -18,15 +18,8 @@ content:
     type: file_default
     weight: 1
     region: content
-  name:
-    label: hidden
-    type: string
-    weight: 0
-    region: content
-    settings:
-      link_to_entity: false
-    third_party_settings: {  }
 hidden:
   created: true
   thumbnail: true
   uid: true
+  name: true
diff --git a/core/profiles/standard/config/optional/core.entity_view_display.media.image.default.yml b/core/profiles/standard/config/optional/core.entity_view_display.media.image.default.yml
index c02d908..eee9348 100644
--- a/core/profiles/standard/config/optional/core.entity_view_display.media.image.default.yml
+++ b/core/profiles/standard/config/optional/core.entity_view_display.media.image.default.yml
@@ -21,15 +21,8 @@ content:
     type: image
     weight: 1
     region: content
-  name:
-    label: hidden
-    type: string
-    weight: 0
-    region: content
-    settings:
-      link_to_entity: false
-    third_party_settings: {  }
 hidden:
   created: true
   thumbnail: true
   uid: true
+  name: true
diff --git a/core/themes/classy/templates/content/media.html.twig b/core/themes/classy/templates/content/media.html.twig
index f36975c..cb65943 100644
--- a/core/themes/classy/templates/content/media.html.twig
+++ b/core/themes/classy/templates/content/media.html.twig
@@ -21,6 +21,7 @@
   ]
 %}
 <article{{ attributes.addClass(classes) }}>
+  {{ title_suffix }}
   {% if content %}
     {{ content }}
   {% endif %}
diff --git a/core/themes/stable/templates/content/media.html.twig b/core/themes/stable/templates/content/media.html.twig
index 769b7be..58732de 100644
--- a/core/themes/stable/templates/content/media.html.twig
+++ b/core/themes/stable/templates/content/media.html.twig
@@ -13,6 +13,7 @@
  */
 #}
 <article{{ attributes }}>
+  {{ title_suffix }}
   {% if content %}
     {{ content }}
   {% endif %}