No, you don't need to set up a database. The WooCommerce hosting comes with a database and WordPress by default. You will be provided phpMyAdmin, a web-based GUI open-source tool, for managing your database for WooCommerce site. WordPress will be automatically installed to your hosting once you confirm the plan. After WordPress is installed, you can log in to add the WooCommerce plugin and start building, editing, and managing your WooCommerce online store.