CREATE OR REPLACE FUNCTION show_users() RETURNS refcursor AS $$
    DECLARE
      ref refcursor;                                   
    BEGIN
      OPEN ref FOR SELECT u_id,u_name FROM usernames;
      RETURN ref;                                      
    END;
    $$ LANGUAGE plpgsql;

                NpgsqlConnection conn = new NpgsqlConnection(GetConnectionString());
                conn.Open();
                NpgsqlTransaction tran = conn.BeginTransaction();
                NpgsqlCommand command = new NpgsqlCommand("show_users", conn);
                command.CommandType = CommandType.StoredProcedure;
                NpgsqlDataReader dr = command.ExecuteReader();
                while (dr.Read())
                {
                    Console.Write("{0}\n", dr[0]); /// 
                }
               // Вывод: одна запись
               //<unnamed portal 1>
               // но данных по бзерам из выборки в функции нет

                if (dr.NextResult()) 
                {
                    Console.WriteLine(@"NextResult");
                    while (dr.Read())
                    Console.Write("{0}\t{1} \n", dr[0], dr[1]);
                }
                else
                {
                    Console.WriteLine(@"NO NextResult");
                }

fetch all from "<unnamed portal 1>" 

  try
            {
                NpgsqlConnection conn = new NpgsqlConnection(GetConnectionString());
                conn.Open();
                NpgsqlTransaction tran = conn.BeginTransaction();

                NpgsqlCommand command = new NpgsqlCommand("show_users_2", conn);
                command.CommandType = CommandType.StoredProcedure;
                command.ExecuteNonQuery();

                command.CommandText = "fetch all in \"<unnamed portal 1>\"";
                command.CommandType = CommandType.Text;

                using (var dr = command.ExecuteReader())
                {
                    while (dr.Read())
                    {
                        // do what you want with data, convert this to json or...
                        Console.WriteLine(@"1) {0}:{1}", dr[0], dr[1]);
                    }
                    //dr.Close();
                }
                command.CommandText = "fetch all in \"<unnamed portal 2>\"";
                command.CommandType = CommandType.Text;

                using (var dr = command.ExecuteReader())
                {
                    while (dr.Read())
                    {
                        // do what you want with data, convert this to json or...
                        Console.WriteLine(@"2) {0}:{1}", dr[0], dr[1]);
                    }
                    //dr.Close();
                }

                tran.Commit();
                conn.Close();
            }
            catch (Exception x)
            {
                Console.WriteLine(x);
            }