Using extern for structures in multiple files

Trying to see how multi-file projects work with structures but I can't figure out why I have an error. I have 2 files test.h and test.cpp. I get a compiler error for test.cpp. It says error 'name' doesn't name a type.

test.h file:

#ifndef TEST_H_INCLUDED
#define TEST_H_INCLUDED

#include <string>

struct Name{
    std::string first_name;
    std::string last_name;
};

extern Name name;
#endif 

test.cpp file:

#include "test.h"
#include<string>

using namespace std;

Name name;
name.first_name= "Jane";