use typeid(class).name
// illustratory code assuming all includes/namespaces etc
#include <iostream>
#include <typeinfo>
using namespace std;
struct A{};
int main(){
cout << typeid(A).name();
}
It is important to remember that this gives an implementation defined names.
As far as I know, there is no way to get the name of the object at run time reliably e.g. 'A' in your code.
EDIT 2:
#include <typeinfo>
#include <iostream>
#include <map>
using namespace std;
struct A{
};
struct B{
};
map<const type_info*, string> m;
int main(){
m[&typeid(A)] = "A"; // Registration here
m[&typeid(B)] = "B"; // Registration here
A a;
cout << m[&typeid(a)];
}