Why members use private listings
As a seller, you might choose to set up private listings when you're selling high-priced items or pharmaceutical products. This is because buyers may not want purchases of high-value items revealed, or may want to keep health-related information confidential.
Unless you've set your listing to private, anyone can see which user bought the item after the listing ends.
How to create a private listing
You can create private listings using the business tool. When creating your listing - opens in new window or tab, simply select Allow buyers to remain anonymous to other eBay users in the Selling details section. When you choose this option, only you can view the usernames of bidders and buyers – they're hidden from everyone else viewing your listing.