Use Contacts For Inbound Calls
Use the contact list to look up callers name and company based on the caller ID. Ideally this could also use the global address book from Exchange but would be fine to just use the local contacts.
Also, when creating a contact associate the call history with the contact so the call history list shows name and company rather than just number.
The fact that there is no integration of a global address book / contact list / phone book or what you may call it, makes it almost impossible to use as a softphone. We have several thousand customer contacts without a possibility to choose them from teams or to find out the caller's name on an incoming call. What's the f*** is wrong with you MS?
Mark Radcliffe commented
Definitely needed for when using an IVR, skype for business could do this!
Contacts and the GAL would be ideal as caller ID does not seem to work with microsoft teams inbound calls