How do bitcoin merchants know that it was YOU that payed them When I try to buy something using bitcoins, how does that merchant know that I have payed them the agreed amount.

In other words, how does the merchant know that I payed for the product, and that they can start shipping the product to me. I thought that bitcoin was anonymous in its transactions
because they most likely generated a new address for you to send your payment to.  Since you're the only one that was given that address, when the payment comes in for that address, they know it was  you that paid it.