The easiest way to make an anonymous online purchase is to buy a gift card at a retail store and pay for it in cash.
Visa, MasterCard, American Express, Discover and JCB sell gift cards in many countries including the United States. They can be purchased in amounts from $25 to $500 at supermarkets, big box stores, pharmacy chains, post offices and many other retailers. No identification is required.
In some countries (Japan, for example) the cards are in the form of paper certificates, but they function the same way.
Once you have a card, simply open the Account & Store tab in Merlin and use it just like a regular credit or debit card to complete your purchase!