fstream zapis nie działa

#include <iostream>
#include <fstream>
#include <conio.h>
using namespace std;

//ZMIENNE*************************************
int menu_glowne;
string name[ 30 ];
string surname[ 30 ];
int phone_number[ 30 ];
int phone_number_person = 1;
int name_person = 1;
int surname_person = 1;
//********************************************
int main()
{
   
    // PLIKI Z DANYMI ***************************
    fstream plik_name( "name.txt" );
    fstream plik_surname( "surname.txt" );
    fstream plik_phone_number( "phone number.txt" );
    //*******************************************
   
    start:
    //MENU GLOWNE********************************
    cout << "[1]-Add person  " << endl;
    cout << "" << endl;
    cout << "[2]-Show the list of persons" << endl;
    cout << "" << endl;
    cout << "[3]-Delete the list of persons" << endl;
    cout << "" << endl;
    cout << "[4]-Search" << endl;
    cout << "" << endl;
    cout << "[5]-Exit" << endl;
    //*********************************************
   
    cin >> menu_glowne;
    switch( menu_glowne )
    {
    case 1:
        {
            //DODAWANIE OSOBY DO LISTY*********************
            system( "cls" );
            cout << "Enter the name of the person" << endl;
            cin >> name[ name_person ];
            cout << name[ name_person ] << endl;
            plik_name << name[ name_person ];
            name_person++;
            cout << "Enter the surname of the person" << endl;
            cin >> surname[ surname_person ];
            cout << surname[ surname_person ] << endl;
            plik_surname << surname[ surname_person ];
            surname_person++;
            cout << "Enter the phone number of the person" << endl;
            cin >> phone_number[ phone_number_person ];
            cout << phone_number[ phone_number_person ] << endl;
            plik_phone_number << phone_number[ phone_number_person ];
            phone_number_person++;
            //*********************************************
            break;
           
        }
    }
    goto start;
   
    getch();
   
    return( 0 );
}