@Thor Bilsby , Following-up from private message. summarizing the answer you shared to benefit the community find the right answer. Since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others ", I' have summarized the answer, request you to "Accept " the answer.
Thanks for your feedback.
This is not possible, as we use a standard Azure domain. While the locator will remain, the Azure Media service (AMS) domain will be shut down, and we will therefore need to change the URL anyway.
Please take a look at this doc - Azure Media Services retirement guide -- guide presents options available for you to migrate to solutions from the Microsoft partner ecosystem or other Azure services.