Open Settings
Tap Notifications
Tap Show Previews
Select When Unlocked or Never
Go back to Settings
Tap Notifications
Tap the app you want to hide name notifications for
Turn off Allow Notifications if needed
Or tap Show Previews and set it to Never for that app
Go to Settings
Tap Face ID & Passcode or Touch ID & Passcode
Enter your passcode
Turn off Notification Center access on the lock screen if needed
Go to Settings
Tap Notifications
Tap Siri Suggestions if needed
Turn off announcement or preview options for messages and calls
Open the Messages app
Tap a conversation
Tap the contact name at the top
Turn on Hide Alerts if you want to silence notifications for that chat