You might be able to achieve your goal by using it in a function, and then examining the function's source with toString()
:
var whatsMyName;
// Just do something with the whatsMyName variable, no matter what
function func() {var v = whatsMyName;}
// Now that we're using whatsMyName in a function, we could get the source code of the function as a string:
var source = func.toString();
// Then extract the variable name from the function source:
var result = /var v = (.[^;]*)/.exec(source);
alert(result[1]); // Should alert 'whatsMyName';