Settings – Tap “Notifications” 
Tap “Messages” 
This is default settings. There are three alert style.
None / Banners / Alerts
Let’s check one by one.
This is how message notification looks like when you choose Banners and it is a default setting.
Tap “Alerts” 
This is how message notification looks like when you choose Alerts.
Tap switch 
to turn off 
in the “Show Previews” on the bottom
This is how message notification looks like when “Show Previews” turned off. As you see, it hides contents of the message. It just says “Text Message“