What is it called when an artist is paid for work to be done?

It depends on why the money is being given.

People who give money to artists because they support the work the artist is doing, while expecting nothing in return, are called Patrons of the Arts.

People who expect the money to be repaid, usually with interest, are called Angels.

People who are buying pieces of art, tickets to performances, etc., are called Clients, Customers, Theatergoers, Concertgoers or whatever applies to the kind of art it is.