Turn off message previews in Settings > Notifications > Messages > Show Previews > Never
Enable Face ID or Touch ID for Messages if your iPhone or app supports it
Use the Hide Alerts option on specific message threads in Messages
Archive or delete sensitive conversations from the Messages app
Use a secure messaging app with app lock or disappearing messages
Turn off message notifications on the Lock Screen in Settings > Notifications > Messages
Disable notification banners and sounds for Messages in Settings > Notifications > Messages
Use Screen Time to restrict access to Messages with a passcode
Keep sensitive chats in a separate account or device if possible
Lock your iPhone with a strong passcode and Face ID or Touch ID