A few questions for you. Where are you looking for the date stamp on the photo after it has been shared? I want to duplicate as closely as possible what you are doing and seeing. To that end, when you share from Lightroom CC's mobile app, are you choosing:
Share>Save Image: or Save to Camera Roll: after you tap on the Share icon?
Also, please supply the iOS version number of your device and the Lightroom CC for iOS version number currently installed.