Good question! I wonder if Amazon would tell. I know with books, even kindle books, there's an option to send anonymously.

I know this because a friend of mine organized a book club where each person was randomly assigned another person to send a book to, but the sender stayed anonymous so the recipient's experience of the book wouldn't be influenced by the identity of the sender. But not knowing the identity of the sender was part of the game so I doubt anyone called Amazon to ask. I wonder if Amazon would tell. It's easy enough to test though.