Teams can only identify callers if the caller number matches one of the Teams user's Exchange/Microsoft 365/Outlook contacts.
This means that the existing corporate contacts must be synchronized with the Teams user's personal contacts. Microsoft then independently and internally synchronizes the contacts between Exchange (Outlook -> People) and Teams (Address Book -> Contacts).
Use sync.blue® to synchronize contacts from countless sources (e.g. weclapp, HubSpot,...) with Teams.