I get a "Maybe:" in front of most iMessage contacts and only the phone number for SMS'es - even for persons from my contact list. What can be the cause and how can I solve it?
This is a Siri Suggestion feature that can be toggled off at Settings > Contacts > Siri & Search > toggle off "Find Contacts in Other Apps".
What is happening is that your device received a message or email from a number or address with a name that could be linked to it, e.g. an email from "John Smith " or a message from a new number that says something like "Hi, this is John Smith."