error LNK2005: already defined - C++

Background

I have a project named PersonLibrary which has two files.

1. Person.h
2. Person.cpp

This library produces a static library file. Another project is TestProject which uses the PersonLibrary (Added though project dependencies in VS008). Everything worked fine until I added a non-member function to Person.h. Person.h looks like

class Person
{
public:
    void SetName(const std::string name);

private:
    std::string personName_;
};

void SetPersonName(Person& person,const std::string name)
{
    person.SetName(name);
}

Person.cpp defines SetName function. When I try to use SetPersonName from TestProject, I get error LNK2005: already defined. Here is how I used it

#include "../PersonLibrary/Person.h"
int main(int argc, char* argv[])
{
    Person person;
    SetPersonName(person, "Bill");
    return 0;
}

Workarounds tried

1 - I have removed the Person.cpp and defined the whole class in Person.h. Error gone and everything worked.

2 - Changed the SetPersonName modifier to static. Like the below

static void SetPersonName(Person& person,const std::string name)
{
    person.SetName(name);
}

Questions

1. Why the code shown first is not working as I expected?
2. What difference static made here?
3. What is the approapriate solution for this problem?

Thanks