How do we move a hybrid domain and users to another Microsoft 365 tenant?

No, renaming the on-premises AD domain is a different operation. Rendom is for renaming a domain within an AD forest, not for releasing a Microsoft 365 domain from one tenant and adding it to another.

Treat this as a tenant-to-tenant migration. Plan the identity and data moves separately from the custom domain cutover. Before the domain can be removed from the source tenant, you will need to resolve objects and services that still reference it, then verify it in the destination tenant. Keeping on-prem AD for existing authentication does not by itself mean you need to rename it.

Start with an inventory before choosing a migration method. Mailboxes, SharePoint, OneDrive, applications, devices and Azure subscriptions can all have different dependencies. In particular, investigate the subscription before assuming the source tenant can be retired.

For Exchange, look at Microsoft's cross-tenant mailbox migration requirements and the hybrid Exchange considerations. Small amounts of SharePoint or OneDrive content might be practical to export manually, but check ownership, permissions and what needs to be preserved first. There is documentation for individual tasks, though not necessarily one runbook that covers every part of this setup.

Don't mix up moving users between tenants with converting synchronized users to cloud-managed users in the same tenant. Disabling directory synchronization can change the source of authority for existing users, but it does not move their accounts or data to the destination tenant.

For any users you intend to convert in place, check the current Microsoft guidance, licensing and Exchange attribute requirements. Verify the users are cloud managed before removing synchronization components. Since AD is still needed for authentication here, plan its eventual retirement as a separate project.

I'd consider getting a migration specialist involved, especially if the subscription or application dependencies are unclear. The right sequence depends on what is actually connected to the source tenant, and a domain cutover can affect more than email.