You can set this to always show a message preview, whether the iPhone is unlocked or not, or only show message previews when the device is unlocked.
However, you can create exceptions for people and apps.
Swipe from right to left to cycle the seven available options, and then from right to left to work back to the beginning of those options.
Try enabling notifications to show alerts and banners from temporary to persistent.
Recover data from iPhone, iTunes and iCloud.
To avoid this repeated alert, you need to mark the message as read.