iPhone saying unknown part after screen replacement

The shop installed the wrong part. They did not use an Apple replacement part for the "repair".

The shop may try to tell you that the part that they used was "just as good" or "the same as" a genuine Apple part. It's not.

When the message about an "unknown part" goes away, you will know that the correct part has been installed. Otherwise, the message will always be on the phone.

If you had the screen replaced ANYWHERE other than Apple or an actual Authorized Service Provider, they don't have access to authentic parts. Only Apple or Apple Authorized Service providers do. So, if you did have it replaced anywhere else, you can certainly take it back to them, but they still won't be in a position to install an authentic Apple screen, so this message will stay with the phone for as long as you own the phone.

If whoever did it is not an Authorized Apple Service Provider, they can NOT fix that. They don’t have legitimate access to genuine Apple parts or the tools required to register them with the system to make that notice go away.

Only Apple or an AASP can do that. You could ask Apple if they will replace the display correctly, but don’t be surprised if they refuse to service your phone at all now that it’s been tampered with.

Yes.