Why is the "for" cycle not creating multiple files?

Why is this code not creating several files? ofstream should create a file when it encounters a file name that doesn't exist. However, for some reason, even though the names are different, it creates only one.

#include <iostream>
#include <fstream>
using namespace std;

int main(void){
    ofstream fout;
    for (int a = 0; a <= 2; a++){
        string name = "test" + to_string(a) + ".txt";
        fout.open(name);
    }
    return 0;
}

Tried switching from "for" to "while" like this

#include <iostream>
#include <fstream>
using namespace std;

int main(void){
    ofstream fout;
  int a = 0;
  while (a <= 2){
    string name = "test" + to_string(a) + to_string(a+1) + ".txt";
    fout.open(name);
    a++;
  }

    return 0;
}

but no result. Also I added another number (a+1) to the name and still got the same result with one created file

You are opening the ofstream but not closing it. the open() method will fail if the stream is already open.

Try this:

ofstream fout;
for (int a = 0; a <= 2; a++){
    string name = "test" + to_string(a) + ".txt";
    fout.open(name);
    fout.close(); // <-- add this!
}

A better option is to simply move the ofstream object inside the loop so it is created and destroyed on each iteration:

for (int a = 0; a <= 2; a++){
    string name = "test" + to_string(a) + ".txt";
    ofstream fout(name);
}