The customer owns the work they purchased, but the artist still holds the copyright. "Artists, since they typically hold the copyright in theses cases, are free to post the work online, make prints of it for sale, and even create a new work based on the original." https://www.plagiarismtoday.com/2019/09/05/copyright-and-commissioned-art

Excuse me!? I have to pay YOU extra to keep MY comission PRIVATE!? If a customer doesn't want you to show off the work they paid for you don't nickel and dime them for More money, you say, "Okay I understand. Thank you for letting me know."