In the Orders Panel (shown in your screenshot) you can click on an order within the list to show the details for that order. The details should show the course names you assigned to the 'products' that were purchased on that order.
Also, if you assign images to each course, you'll see a thumbnail of this in the column to the right of the order number, making it easy to see who ordered which course by glancing at the list.
You can also track purchases in the Analytics Panel but Squarespace does not provide a way to select a product/course and list the relevant orders to know who purchased it.
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