Howdy,
If you can't find where an AirDropped item went on your iPad…
How to use AirDrop on your iPhone, iPad, or iPod touch states
If you AirDrop something to yourself, like a photo from your iPhone to your Mac, you won't see an option to Accept or Decline — it'll automatically get sent to your device.
and
AirDrop will come through within the same app it was sent from. For example, photos appear in the Photos app and websites open in Safari
So check the similar App from where it was sent or maybe the Files App.
If you still can't find it and remember the name, search for the file by dragging down from the middle of the Home Screen to get the search field.
If you still can't find it, try AirDropping a similar known file again and search for that. You may find where they are going.
ivan