And you can have more or less anonymous companies in US.

So ...

Companies aren't anonymous in the US. Corporations must have registered agents in each state in which the corporation is registered, the name and address of whom is public in order to facilitate service of process. LLCs in most states must include at least one member, manager, organizer, or authorized individual in the public filing, and even in states that don't require this, a bank will want it in the public paperwork before opening an account in the LLC's name.

A company must have a registered agent; that registered agent may not be the beneficial owner of the company and could be someone's attorney.

Obviously you’ve never registered a company in any state in the US.