Everything in JS is bound to containing scope. Therefore, if you define a function directly in file, it will be bound to window object, i.e. it will be global.

To make it "private", you have to create an object, which will contain these functions. You are correct that littering global scope is bad, but you have to put something in global scope to be able to access it, JS libraries do the same and there is no other workaround. But think about what you put in global scope, a single object should be more than enough for your "library".

Example:

MyObject = {
    abc: function(...) {...},
    pqr: function(...) {...}
    // other functions...
}

To call abc for somewhere, be it same file or another file:

MyObject.abc(...);

You could instead call it as window.getNameField:

alert(window.getNameField().value);

Or you could define a variable outside the closure:

var getNameField;

(function(){
    getNameField=function(fieldId){
        // Code here...
    };
}());

alert(getNameField().value);