iPhone not showing received texts?

I often turn my iPhone 6 off overnight. If I receive a text while it has been turned off, when I turn the phone on again I get a notification on the lock screen, but when I go to open Messages the text isn’t there and never appears. Also, even if the text has come from someone in my contacts, the notification on the lock screen is always from their phone number rather than their name. This doesn’t happen with direct messaging such as iMessage, WhatsApp or Facebook messaging, just with texts. Obviously this is a problem when I can see on the lock screen that I’ve been sent an important text, but as soon as I unlock my phone it’s gone forever.