If all that is needed is a high degree of privacy, I think simply discussing with management to ensure that one’s presence at the hotel is never acknowledged to any third party or outside caller would be sufficient.

If this really is a security issue, then further layres of protection could be implemented. Staying under an alias could be orchestrated by management/security in order to shield guest’s true identity from hotel personnel who do not need to know. Other options could be secure entrance and exit, special suite allocation for privacy, movement by service elevators, etc...