This app was mentioned in 2 comments, with an average of 3.50 upvotes
Already a thing, at least on Android. https://play.google.com/store/apps/details?id=com.ciamedia.caller.id
This thing looks up online phone books for details of your caller and shows it 1-2 sec after the phone starts ringing.
Had it on my phone but never got any calls, so I've uninstalled it again.
//edit: depends on your location as well. worked fine back then in Austria, EU.
I'm using CIA (I know, weird name!) - they didn't ask to upload anything, but do ask for lots of permissions as well. But I went to their website and they explain them all in their faq, so I'm not too worried. It works pretty well but not on unlisted numbers either... https://play.google.com/store/apps/details?id=com.ciamedia.caller.id