Is there a word for payments made to freelance workers such as designers?

Solution 1:

Although the terms payment (“A sum of money paid in exchange for goods or services”) and fee (in the sense “monetary payment charged for professional services”) don't refer specifically to payments made to freelance workers – ie, are more general than that – they are, nonetheless, correct terms for such payments. Commission (“A fee charged by an agent or broker for carrying out a transaction”), on the other hand, is overly specific and does not apply to most payments made to freelance workers. In addition, many salaried and non-freelance workers receive commissions based on percentages of sales.

Other terms that may be relevant are shown below. The first two terms denote specialized kinds of payments, while the other two are nearly synonymous with payment.
• stipend, “a fixed payment, generally small and occurring at regular intervals; a modest allowance”, which may apply in some cases;
• retainer, “A fee one pays to reserve the other's time for services. [eg] This lawyer charges a retainer for his work”
• emolument, “A salary, fee, or profit from employment or office: [eg] the directors' emoluments”
• remuneration, “A payment for work done; wages, salary, emolument”

Solution 2:

Commission is an appropriate word for it. Most artists online are commissioned by various users (patrons) on whatever sites they (the artist) happens to frequent. Patronage is another appropriate word, but it is somewhat dated. If only in the US, most people use it to refer to payments made to any business, not necessarily an artist.