Welcome to Apple Support Communities.
If I'm understanding correctly, the callers contact info is not displaying when you receive their call. Knowing who is calling you is important, and I'll be glad to help. To get started, do you sync your contacts with iCloud? If so, let's make sure that they are turned on.
The steps below will walk you through checking this, from our article: Get help using iCloud Contacts, Calendars, or Reminders
On your iPhone, tap Settings > [your name] > iCloud. (If you're using iOS 10.2 or earlier, tap Settings > iCloud.) Check your Apple ID and make sure that you turn on what you want to update (Contacts, Calendars, or Reminders).
Let us know how it goes.