Set the origin of custom templates to 'plugin' and fix plugin name on…

… REST requests (#5375)

* Set the origin of custom WC templates to 'plugin'

* Fix plugin name

src/Utils/BlockTemplateUtils.php

@@ -116,6 +116,11 @@ public static function gutenberg_build_template_result_from_post( $post ) {
 			}
 		}
 
+		if ( 'woocommerce' === $theme ) {
+			$template->theme  = 'woocommerce/woocommerce';
+			$template->origin = 'plugin';
+		}
+
 		return $template;
 	}
 
@@ -133,7 +138,7 @@ public static function gutenberg_build_template_result_from_file( $template_file
 		$template_content         = file_get_contents( $template_file->path );
 		$template                 = new \WP_Block_Template();
 		$template->id             = 'woocommerce//' . $template_file->slug;
-		$template->theme          = 'WooCommerce';
+		$template->theme          = 'woocommerce/woocommerce';
 		$template->content        = self::gutenberg_inject_theme_attribute_in_content( $template_content );
 		$template->source         = 'plugin';
 		$template->slug           = $template_file->slug;