How do I decorate this and what is it called?

Cathedral ceiling wall bridge. That's hard, anything you do just becomes a cleaning nightmare. I'd just add some accent color and let it be.

Not really sure what area of the house this is by looking at your picture.

If a bedroom then personal items that are not breakable if they fall, like a stuffed animal collection.

If a family room then maybe attach a horizontal pipe and hang a series of pictures or large charts or maps.

My only other thought would be to put up a seasonal or holiday theme that you could readily take down and move onto the next.

For example a wreath or a garland at Christmas.

Kelli had a good idea with paint, use the bridge to break the color scheme up with a contrasting color.

Looks like a good place for uplighting to me. Put some objects up there to cast shadows even. A LED light string on a remote will work so you don't have to climb up and down to turn it on and off.

I'd cut weathered wood planks that have been color washed in a pretty color then the color sanded off here and there for the back of it (think old barnwood), then get 3 or 4 canning jars with lids and put some of the remote control fairy lights in them. Then maybe a piece or two of something rustic as well to go between the jars- maybe a small basket of some sort (wire egg basket?) with a silk ivy vine in it at the center point.

This would be a great place to display a quilt threaded through a wood ring or frame.

Just think of How you are going to keep everything clean and dusted up there...That will answer your Question..-I would leave it empty or just put some odd Crocks or boxes up there..

It's a "plant ledge" according to the builder of my former house. Put a big faux flower arrangement on it? I had a big vintage advertising sign on it.

Maybe you can crochet a dream catcher and hang it up there.

Lots of great ideas! It definitely needs a darker contrasting color and simple decor. I like the ideas of old rusty things, vintage signs or barn wood because they “blend” with dust. Lol!

I agree. Put something up there which you only dust or clean annually. A bright blanket, quilt depending on whether you like a Native American, Country, or Ball Park type theme? Large pottery and or vases. Galvanized buckets or farm implements with bright silk flowers?

I would paint a complementary color and call it done. It is going to be a nightmare to keep anything clean and dust free. Then you can always vacuum or use a swifter to clean without removing items.