Class Problem

[Technocrat]

I am not sure how to ask this but here it goes; Lets say I have a class:

class FILE
{
  public:
    std::string sName;
};

Then I use it:

FILE f1;
FILE f2;
f1.sName = "Test.txt";
f2.sName = "Test2.txt";

What I want is to check and make sure this doesnt happen. I want to ensure that each class has a unique sName. So how can I check or ensure this doesnt happen?