Amazon’s Wishlist may notify you on the item’s page when someone’s purchased an item on your list. You can also see by selecting “Purchased” or “Purchased and Unpurchased” from the “Filter & Sort” drop-down menu at the top of your list.
To change your Purchased Item filter settings;
Note: The Purchased Item filter and warnings only appear when you're logged in to your account.
If you create a gift list, then choose the “Don’t spoil my surprises” option. The "Don't spoil my surprises" setting is on default so your gift purchases will remain secret for several weeks. It will continue to appear as “Unpurchased” during this period.
If you try to buy an item that has already been gifted, you should receive a warning to protect you against duplicate purchases.