Based on some other incoming features (like rebinding existing projects), I think there will finally be some movement on this soon. And, for now, it’s currently not possible to unbind an organization and bind it to something else. You can vote for adding this feature here.
The only way to have your organization bound to an Azure DevOps organization with a different name is to create a new organization and re-import your repositories there. Unfortunately, that means you’ll lose the results of previous analyses on these projects.
If you have a yearly subscription for your current organization, a new coupon can be issued for your new organization by reaching out to your sale representative.
If you have a monthly subscription by credit card, you can simply stop your subscription on the old organization and re-subscribe on the new one.
That’s disappointing to say the least… I’m glad that you are looking at implementing this feature in the future.
If you would allow a follow-up question, does this also mean that if we decide to migrate to a new DevOps platform (let’s just say Github Enterprise) we also can’t rebind our SonarCloud organization to the new (Github) organization?