string.size() always returns 0

I'm trying to write a program that returns the number of characters in a string. As I was writing my program, I've noticed that there's a bug in the string class. The length always returns 0.

Say my program is this:

#include<iostream>
#include<cstring>
#include<string>

using namespace std;

int main()
{
    string fname;
    string lname;
    string fullname = fname + lname;
    int length=fullname.size();
    cout<<"Name Registration";
    cout<<"\n\nPlease Enter your first name";
    cin>>fname;
    cout<<"\n\nPlease Enter your Last name\n";
    cin>>lname;
    cout<<"\n\nYour Full Name is "<<fname<<" "<<lname<<".\n\nYour Name contains "<<length<<" words";
}