diff --git a/wp-admin/site-editor.php b/wp-admin/site-editor.php
index cbbf38e7ea..7706595172 100644
--- a/wp-admin/site-editor.php
+++ b/wp-admin/site-editor.php
@@ -49,7 +49,7 @@ foreach ( get_default_block_template_types() as $slug => $template_type ) {
 	$indexed_template_types[] = $template_type;
 }
 
-$block_editor_context = new WP_Block_Editor_Context();
+$block_editor_context = new WP_Block_Editor_Context( array( 'name' => 'core/edit-site' ) );
 $custom_settings      = array(
 	'siteUrl'                              => site_url(),
 	'postsPerPage'                         => get_option( 'posts_per_page' ),
diff --git a/wp-admin/widgets-form-blocks.php b/wp-admin/widgets-form-blocks.php
index 563bbf2a69..ee3cb37734 100644
--- a/wp-admin/widgets-form-blocks.php
+++ b/wp-admin/widgets-form-blocks.php
@@ -15,7 +15,7 @@ if ( ! defined( 'ABSPATH' ) ) {
 $current_screen = get_current_screen();
 $current_screen->is_block_editor( true );
 
-$block_editor_context = new WP_Block_Editor_Context();
+$block_editor_context = new WP_Block_Editor_Context( array( 'name' => 'core/edit-widgets' ) );
 
 $preload_paths = array(
 	array( rest_get_route_for_post_type_items( 'attachment' ), 'OPTIONS' ),
diff --git a/wp-includes/class-wp-block-editor-context.php b/wp-includes/class-wp-block-editor-context.php
index 92957f3bd8..fd594bcad0 100644
--- a/wp-includes/class-wp-block-editor-context.php
+++ b/wp-includes/class-wp-block-editor-context.php
@@ -7,17 +7,29 @@
  */
 
 /**
- * Class representing a current block editor context.
- *
- * The expectation is that block editor can have a different set
- * of requirements on every screen where it is used. This class
- * allows to define supporting settings that can be used with filters.
+ * Contains information about a block editor being rendered.
  *
  * @since 5.8.0
  */
 final class WP_Block_Editor_Context {
 	/**
-	 * Post being edited. Optional.
+	 * String that identifies the block editor being rendered. Can be one of:
+	 *
+	 * - `'core/edit-post'`         - The post editor at `/wp-admin/edit.php`.
+	 * - `'core/edit-widgets'`      - The widgets editor at `/wp-admin/widgets.php`.
+	 * - `'core/customize-widgets'` - The widgets editor at `/wp-admin/customize.php`.
+	 * - `'core/edit-site'`         - The site editor at `/wp-admin/site-editor.php`.
+	 *
+	 * Defaults to 'core/edit-post'.
+	 *
+	 * @since 6.0.0
+	 *
+	 * @var string
+	 */
+	public $name = 'core/edit-post';
+
+	/**
+	 * The post being edited by the block editor. Optional.
 	 *
 	 * @since 5.8.0
 	 *
@@ -35,6 +47,9 @@ final class WP_Block_Editor_Context {
 	 * @param array $settings The list of optional settings to expose in a given context.
 	 */
 	public function __construct( array $settings = array() ) {
+		if ( isset( $settings['name'] ) ) {
+			$this->name = $settings['name'];
+		}
 		if ( isset( $settings['post'] ) ) {
 			$this->post = $settings['post'];
 		}
diff --git a/wp-includes/class-wp-customize-widgets.php b/wp-includes/class-wp-customize-widgets.php
index 8edcd6f1c9..1b6fe0a610 100644
--- a/wp-includes/class-wp-customize-widgets.php
+++ b/wp-includes/class-wp-customize-widgets.php
@@ -838,7 +838,11 @@ final class WP_Customize_Widgets {
 		 */
 
 		if ( wp_use_widgets_block_editor() ) {
-			$block_editor_context = new WP_Block_Editor_Context();
+			$block_editor_context = new WP_Block_Editor_Context(
+				array(
+					'name' => 'core/customize-widgets',
+				)
+			);
 
 			$editor_settings = get_block_editor_settings(
 				get_legacy_widget_block_editor_settings(),
diff --git a/wp-includes/version.php b/wp-includes/version.php
index e8693c7347..4b0a6d97d0 100644
--- a/wp-includes/version.php
+++ b/wp-includes/version.php
@@ -16,7 +16,7 @@
  *
  * @global string $wp_version
  */
-$wp_version = '6.0-alpha-52941';
+$wp_version = '6.0-alpha-52942';
 
 /**
  * Holds the WordPress DB revision, increments when changes are made to the WordPress DB schema.