I've created an application with AppleScript in Automator.
When I was saving the application, I made sure that the "Hide extension" box was unchecked, like so:
But once the application was saved, the extension did not appear after the filename in Finder.
When I right-click on the file in Finder and click Get Info, I am presented with the following:
After unlocking the padlock in the bottom-right corner of the Get Info window, the "Hide extension" box is still greyed out.
I have also tried renaming the file by pressing Enter while the file is selected in Finder, and manually appending ".app" to the end of the filename. Although I am able to successfully do so without triggering an error message, the ".app" bit is removed from the filename instantly.
Best Answer
I believe that the System automatically by default hides the .app filename extension regardless of unchecking the Hide extension checkbox upon being saved and the Hide extension checkbox on the Get Info sheet will be grayed out when the .app filename extension is present. You'll need to send feedback to Apple on this one.
The only way I know how to override this in Finder is to check the Show all filename extensions checkbox under Advanced Finder Preferences. This of course then shows all filename extensions that are set to hidden, not just the .app filename extension.