Changing the program it opens with doesn't change anything about the file itself.
What you've run into is Microsoft's bone-headed, but well-intentioned decision, starting with Windows 95, to hide File extensions. What happens is basically if Windows knows how to open a file, it won't show the extension at all, otherwise, it will.
The dialog you saw basically sets the association, so from that point forward, Windows knows how to open the file, so it is presented without a file extension. Additionally, the icon will change to show a little image of the associated program inside the default page.
The "fix" is effectively to do nothing- nothing about the file is changed, it merely opens with notepad by default.