Sample.cs

using System;

namespace visibility
{
    public class Sample
    {
        public static void Main (string[] args)
        {
            User user = new User("Neto");

            User.changePrivateName(user, "João Batista Neto");
            
            user.showPrivateName(); //João Batista Neto
        }
    }
}

User.cs

using System;

namespace visibility
{    
    public class User
    {
        private String privateName;

        public User(String name)
        {
            privateName = name;
        }

        public static void changePrivateName(User user, String name)
        {
            user.privateName = name;
        }

        public void showPrivateName()
        {
            Console.WriteLine(privateName);
        }
    }
}