Extend Woocommerce Widget Class – WC_Widget_Product_Categories

When calling parent::__construct() from WC_Widget_Product_Departments the constructor of WC_Widget_Product_Categories immediately overwrites the class properties (especially the widget_id), see here at GitHub. So you have to extend WC_Widget to create a new widget and then you can copy anything what you need in your widget from WC_Widget_Product_Categories to WC_Widget_Product_Departments.