According to the response in https://developer.apple.com/forums/thread/735022, it depends on whether your apps are published to the App Store or not. For an App Store app, the system uses the associated iCloud container ID to retrieves the app name and icon from the App Store. For an app that isn't in App Store and is installed with Xcode, the system uses the last component of the iCloud container ID as the app name, and the Xcode-generated icon. However, replacing the container or changing app's metadata in the App Store is likely not an option.

I encountered a similar issue but, unfortunately, did not have any backup data available. While attempting to recover the lost data, I noticed an intriguing inconsistency: Some devices running older OS versions (unsupported by my app), but linked to the same Apple ID, display the container with a larger size (as if some data was preserved) compared to devices that had the app installed before the data was purged. On an older Mac, I run ls -a to list containers in ~/Library/Mobile Documents and obtained a comprehensive list of various containers. Unfortunately, mine CloudKit container was not present in that directory, but was visible in System Settings->iCloud->Manage Storage. I am curious how it is possible for some devices to reference the same container but display different sizes. Is it possible to access the preserved data, assuming it is cached? Any suggestions on where to look would be greatly appreciated!