Thanks for reaching out to the Apple Support Communities.
I understand that when you receive an incoming call it's not always showing that there is an incoming call on your display. The phone will only ring and vibrate. It's important to make sure that you can see who is calling, so I'm happy to provide some support.
It sounds like the Phone app on your iPhone isn't responding like it should. I suggest a close of the Phone app and a restart of your iPhone to see if this helps the issue.
How to force an app to close on your iPhone, iPad, or iPod touch
Restart your iPhone, iPad, or iPod touch
Also check to make sure that your iPhone is running the latest update. If there is a case on the iPhone or any accessories connected, please remove and test.
Once you've done these steps, let me know if you get the same result.