How do I cover up holes on damaged doors?

Hello -could you possibly post a picture to give us an idea of the extent your damage. Sometimes patching with wood putty works. Sometimes you need the patching material if it is a sizable hole.

Kathy, I would consider covering the holes with tin stars of different sizes to mask the original damage to the door. I believe this design element will compliment your door. You could get different types of tin metal stars in an approximate size to mask the original damage to the door. Be creative here. Antique your stars, or spray paint and wipe off some of the paint to make it look “antiqued”. You can find stars or whatever you want in a craft store. Shop around with your color scheme and measurements. Don’t forget the glue! Good luck!

It sounds like you have a hollow core door? This will require wood putty, but you will also need to place a supporting backer behind the damage. If it's big enough to put your hand through, place a piece of Luan or similar product inside the door cavity and glue it to the back side of the damaged area with construction adhesive. Once dried, use wood putty in thin layers to gradually build up the surface to match the original surface. Sand smooth and prime, then paint.

https://www.queenbeeofhoneydos.com/repair-hollow-core-door/

https://www.youtube.com/watch?v=4K233OoNfKk