Open the Settings app on your iPhone
Tap Notifications
Tap Announce Notifications
Turn off Announce Notifications
To stop only Messages, tap Messages under Announce Notifications and turn it off
Open the Watch app if needed and turn off Announce Notifications there too
Open Control Center while wearing AirPods and tap the Announce Notifications icon to disable it
Ask Siri to turn off Announce Notifications
If needed, go to Settings
Tap Siri & Search
Turn off Announce Notifications with Siri