If your notifications on your iPhone do not show a full preview of the content on your lock screen, you can change this as follows:
By default, iPhones with Face ID hide the content preview for notifications until they can be verified. This is not such a big deal because Face ID is super fast and almost instant. However, if you have your iPhone on your desk and in a position where Face Detection does not work, you will need to pick up your iPhone and verify your face after receiving a notification to see the preview.
The good news is you can always change this to show the content of the notification, and it's just a quick switch between settings.
Open the Settings app on the Home screen.
Select "Show Previews" above.
From now on whenever you receive a notification, the content preview is always displayed, regardless of whether your iPhone is locked or unlocked. This does not have to be checked first with the Face ID.