No, You cant modify the incoming call screen of CallKit. But when user receives the call, the control get handled over to your own app, where you can show whatever you want for currently running app(just like whatsapp, skype etc).
For Incoming call screen, you can only show the values that are in CXCallUpdate
(https://developer.apple.com/documentation/callkit/cxcallupdate). Here, you can modify user's localized name, remoteHandle(for showing phonenumber/email address of the caller), and you can give boolean values to other properties of CXCallUpdate
based on what your call supports. Thats it.
You might have checked all other VOIP call apps, you must not have found any app having custom incoming call screens(If by chance if they have, then it must not be working in background, I mean it must not be working in combination with PushKit).