Got it. If anyone out there comes to this problem, what you can do is use popUpOpen or popUpClose FileManager
methods in JavaScript to get HTML div element of the rename popup dialog and get the input field or button contents like so:
function popUpClose(args){
if (args.popupName == 'Rename') {
var arr = [].slice.call(args.popupModule.element.getElementsByTagName('input'));
alert(arr[0].value);
}
}
It's an ugly way to do it, but you get the gist of it.