I have a client that changed its business name, and with it the domain. For example: oldcompany.com into newcompany.com. Legally, they stayed the same entity, owning both domains.
Now they have migrated most of their GCP resources to match the new name, however the GCP organisation itself remained on oldcompany.com.
As time passes, they want to turn off their oldcompany.com domain. I could not answer their question, on how to change the domain for a GCP organisation.