Turn off message previews: Settings > Notifications > Messages > Show Previews > Never
Hide alerts for a specific conversation: Messages > open chat > tap contact name > Hide Alerts
Use Focus mode to silence Messages: Settings > Focus > choose a Focus > Allowed Notifications > Messages
Filter unknown senders: Settings > Messages > Filter Unknown Senders
Hide message notifications on Lock Screen: Settings > Notifications > Messages > uncheck Lock Screen
Disable banner alerts for Messages: Settings > Notifications > Messages > Banner Style > None
Turn off notification badges for Messages: Settings > Notifications > Messages > Badges off
Delete the conversation from Messages: swipe left on the thread > Delete
Use a separate iCloud account or device for private messages
Lock the Notes app or use a secure messaging app for sensitive texts