If you have a Shopify store, the eBay order number will appear in the ‘order note’ section.

The order will also have an ‘eBay’ Tag in the tag section on the order details page.

For Big Commerce stores, you will see ‘external’ noted as the source of the order. 

NB: Orders are considered to be made by a ‘Guest’ in your store as the customer buying from you has not logged into your store to purchase.