Add author name to term name

And sync it with display name

inc/namespace.php

@@ -47,6 +47,7 @@ function bootstrap() : void {
 	add_action( 'pre_get_posts', __NAMESPACE__ . '\\action_pre_get_posts', 9999 );
 	add_action( 'wp', __NAMESPACE__ . '\\action_wp' );
 	add_action( 'wp_insert_post', [ $insert_post_handler, 'action_wp_insert_post' ], 10, 3 );
+	add_action( 'profile_update', __NAMESPACE__ . '\\update_author_term_name', 10, 3 );
 
 	// Filters.
 	add_filter( 'wp_insert_post_data', [ $insert_post_handler, 'filter_wp_insert_post_data' ], 10, 3 );
@@ -59,6 +60,32 @@ function bootstrap() : void {
 	add_filter( 'comment_notification_recipients', __NAMESPACE__ . '\\filter_comment_notification_recipients', 10, 2 );
 }
 
+/**
+ * Sync author term name with user display name.
+ *
+ * @param int     $user_id User ID.
+ * @param WP_User $old_user_data Old user data.
+ * @param array   $userdata User data.
+ * @return void
+ */
+function update_author_term_name( int $user_id, WP_User $old_user_data, array $userdata ) : void {
+	// User doesn't exist in authorship taxonomy.
+	$term = get_term_by( 'slug', (string) $user_id, TAXONOMY );
+	if ( ! $term ) {
+		return;
+	}
+
+	$display_name = isset( $userdata['display_name'] ) ? $userdata['display_name'] : '';
+	// User display name hasn't changed.
+	if ( $term->name === $display_name ) {
+		return;
+	}
+
+	wp_update_term($term->term_id, TAXONOMY, [
+		'name' => $userdata['display_name'],
+	]);
+}
+
 /**
  * Return list of supported post types, defaulting to those supporting 'author'.
  *