When setting up your Products in your Stripe Dashboard and want to prevent the Payment app showing the "price_xxxx" identifiers, you will need to add a Price description for each Price.
Once you've set all of the price descriptions for each price, the Payment app will then organize and group these prices based on the top level product (e.g. Shirts) and all of the Prices (e.g. sizes, styles, etc).
To further describe your products, you can add additional "metadata" to a Price. This will modify the Products list in the app to show short descriptions under each Price Description. To do this, you'll need to navigate to your Product, then click the row for the specific Price you'd like to edit.