Rant: You appear to be depending on JavaScript (you almost certainly don't need to as you can do most things server side), and depending on the browser creating a global variable reference to any element with an id or name (which boils down to assuming the user has Internet Explorer without the security settings ramped up).

As to getting the names of the form fields:

the param() method will return the parameter names as a list

... that's what is supposed to happen. You should probably reread the docs for CGI.pm.