After changing the client on a project, the existing invoices still display the old client instead of the new one.
When you update the client on a project, Core prompts you to update the client on previous invoices and payments as well. But if you choose No for the prompt, the client details remain unchanged on the old invoices. If you want to update the details on them, you should temporarily update the client on the project again in the Project Details > General > Details screen to something different and then choose No for the prompt. After that, update the client to the actual one and this time choose Yes for the prompt. Core updates all previous invoices and payments with the new client.