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.
For WooCommerce the "note" field in the order contains the name of the marketplace the order came from, alongside the marketplace order number. It will show under "Customer provided note" on the order screen. For versions of WordPress version 4.4.0 or higher and WooCommerce version 2.6.0 or higher, you can also add the tag 'eBay' into a custom field of your choosing under Settings > Feeds > General in "Sales channel field" which can then be accessed as a distinct field in the order in WooCommerce.