Is there a word to describe someone that receives a bill?

When a client of mine offers their services, they have to determine to whom to send the bill. Is there a word to describe that person/organization?

While not in many dictionaries I've often heard the word invoicee: one who receives the invoice.

You might also just refer to them as the Buyer or the Purchaser

They would be the recipient of the bill.

You might refer to responsible party, to the payer ("One who pays; specifically, the person by whom a bill or note has been, or should be, paid"), or conceivably to the debtor ("A person or firm that owes money; one in debt; one who owes a debt"). Online payment forms often have a section for billing address information that can include the name of the party responsible for payment.

There is also the common billing term: Responsible Party.