How to call a function by its name (std::string) in C++?

What you have described is called reflection and C++ doesn't support it. However you might come with some work-around, for example in this very concrete case you might use an std::map that would map names of functions (std::string objects) to function pointers, which in case of functions with the very same prototype could be easier than it might seem:

#include <iostream>
#include <map>

int add(int i, int j) { return i+j; }
int sub(int i, int j) { return i-j; }

typedef int (*FnPtr)(int, int);

int main() {
    // initialization:
    std::map<std::string, FnPtr> myMap;
    myMap["add"] = add;
    myMap["sub"] = sub;

    // usage:
    std::string s("add");
    int res = myMap[s](2,3);
    std::cout << res;
}

Note that myMap[s](2,3) retrieves the function pointer mapped to string s and invokes this function, passing 2 and 3 to it, making the output of this example to be 5

Using a map of standard string to standard functions.

#include <functional>
#include <map>
#include <string>
#include <iostream>

int add(int x, int y) {return x+y;}
int sub(int x, int y) {return x-y;}

int main()
{
    std::map<std::string, std::function<int(int,int)>>  funcMap =
         {{ "add", add},
          { "sub", sub}
         };

    std::cout << funcMap["add"](2,3) << "\n";
    std::cout << funcMap["sub"](5,2) << "\n";
}

Even better with Lambda:

#include <functional>
#include <map>
#include <string>
#include <iostream>

int main()
{
    std::map<std::string, std::function<int(int,int)>>  funcMap =
         {{ "add", [](int x, int y){return x+y;}},
          { "sub", [](int x, int y){return x-y;}}
         };

    std::cout << funcMap["add"](2,3) << "\n";
    std::cout << funcMap["sub"](5,2) << "\n";
}

There is another possibility which hasn't been mentioned yet, which is true reflection.

An option for this is accessing functions exported from an executable or a shared library using operating system functions for resolving names to addresses. This has interesting uses like loading two 'contestant' dlls into an 'umpire' program, so that people can slug it out by having their actual codes fight each other (playing Reversi or Quake, whatever).

Another option is accessing the debug information created by the compiler. Under Windows this can be surprisingly easy for compilers that are compatible, since all the work can be off-loaded to system dlls or free dlls downloadable from Microsoft. Part of the functionality is already contained in the Windows API.

However, that falls more into the category of Systems Programming - regardless of language - and thus it pertains to C++ only insofar as it is the Systems Programming language par excellence.