Since you don’t have a G-Suite account you might need to sign-up Cloud Identity services in-order to create an Organization resource. Once you signed up, you can set-up your own organization by following this documentation. Please note that to be able to change your organization name you will need to buy a domain name, as this is required by Cloud Identity.
For better understanding on Google Cloud Platform(GCP) resource hierarchy, you can further check this help center article as well.