Display only shows number/e-mail adress

Went back from android to iPhone 6 on Saturday.

Turned the phone on, did the usual things to set up the phone and voila, already text messages (both iMessage and sms) shows as either telephone number or e - mail adresses but only on some..

What I've tried so far:

- Hard reset

- On/off

- Logged in/out iCloud

- Resetting network

- Toggled iCould contacts off

- Asked Siri

- Switched off dial assist

- Made sure the location and iMessage cooperates

- Banged head in desk several times.............

Any other suggestions?!