What rights does an artist have over how their work is changed or credited?

Selling the physical artwork does not transfer the copyright unless you assign it, and you may also have moral rights under the Copyright Act 1994. These include the right to be identified as the author, which must be asserted, and the right to object to derogatory treatment of your work, which includes any distortion or mutilation that is prejudicial to your honour or reputation. Cutting a painting in half could potentially amount to derogatory treatment, although the right is limited, and the owner of the physical work may have other rights, so the outcome is not certain. You can send a letter requesting that they stop and disassociate your name from altered pieces. Separately, the Resale Right for Visual Artists Act 2023 gives visual artists a royalty on certain later resales of their work through art market professionals, so check whether it applies. Take legal advice.