My answers consist of Offshore in Mauritius only (Applicable for other Jurisdictions also).
In Mauritius you have Owners sometimes referred to as Ultimate Beneficial Owners or Beneficial Owners. These are different from Members (Shareholders /Nominee Shareholders). A shareholder will hold shares in the Company and names will appear in all documents. An Ultimate Beneficial Owners will form a trust with the shareholders specifying each and very details of their authority in the Company.
Moreover, to open an offshore company in Mauritius, it is mandatory that you reveal your identity to the Financial Services Commission.
This applies for banks also, where you will be asked to provide all details of the shareholders and ultimate beneficial owners. Without it, they would categorically not accept you.
Unfortunately, I cannot post link here, otherwise I would post all the links from regulatory boby (Bank of Mauritius, Registrar of Companies, Financial Services Commission and Financial Intelligence Unit) there to support my answers.
However, I do agree that going offshore is not a game. You need to play with all the cards. That’s why I always strongly advise my client to choose an agent first.