There are a few pointers. YOu are not sure the make.
Remove the lower grill (The one on the ceiling) and shine a flashlight UP and see if there is a label.. It may be there or it may be topside under the shroud but if you find the label the manufacturer's name may be on it.
Now Vizone RV in KY (not sure about that e) if you happen to be near them (They are in southern KY off (I-75) they may be able to identify the Unit and even provide a used (or new) shroud..
They are ONE such facility. Look them up and see if there is a competitor near you once you know what you are looking at (RV Graveyard)
You can patch the hole with Eternabond if you like or if it's small GOOP.