The only way I know to pay anonymously with PayPal is to have the recipient generate a barcode from Her account using the "add cash" option. She then emails the barcode to you and you have one hour to go to a pre-selected retailer (CVS, Walmart, etc) that She has selected. You can go to any location of said retailer, you show the barcode to the cashier, tell them the amount, and pay them in cash. They will scan the barcode and the recipient will get the funds in about 15 minutes. Its anonymous for both sender and recipient as the barcode does not contain any identifying information.