The pages related to WooCommerce (e.g. the order details page) don’t display the listing title in the current Claim Listings version. We’ll try to improve this, but the customers select a listing manually thus knowing which listing is about to be claimed, and the claim created for order also contains this info (in the back-end Listings/Claims section).
Please make sure that the payment methods are set up correctly, gateways like Stripe or PayPal should mark orders as Processing/Completed automatically, and if this status is set the claim will also be approved automatically (switching the listing author).
Hope this helps.