In the US, you can stay 100% anonymous using shell corporations, but it's fairly expensive to set up and requires some discipline from anyone who knows the secret.
Except you will have to disclose ownership for KYC requirements to financial institutions, and for the new BOI yearly filing in the US.
That's not a feature of a shell corporation, but of agent listings where incorporated such as Delaware series LLCs. One way would be to have an S corp that owns a series LLC.