The following behaviour can be expected when you make changes to the name of a backed-up Microsoft tenant.

Domain name change to existing Microsoft tenant:

When you change the domain name of a backed-up Microsoft tenant, the component IDs associated with the users (accounts) on the tenant remain unchanged. All backup and restore operations will continue to function as expected.

Addition of a new Microsoft tenant:

When the name change is because an entirely new tenant is being added, our system cannot link the new tenant to the original tenant (and its users/accounts). In this case, a new backup set must be created to ensure backup and restore operations continue to function as expected.