How can I change the icon, icon name that lays under the icon, notification name, and notification icon for an Android app?
You need an apk editor. With it you can edit app,so change icons etc.,but you also need to change JSON file becaose app need to know which file it need to use. After you edit app, you need to sign it,  most app editors do it automaticly. And then install like update over app. But there is a problem. Some apps will after update return to original settings. And some will give you notice that app is edited and forbid you from using it. So all dependent on app. You did not specify your device manufacter, but if you have Samsung you can change icons of most apps in Samsung Theme app(some thems can change app icon design and notification iconand you can also  download only app icon design). 

If you only want to "edit" app you need to be vety carefully to not ruin app completly. Good Luck.