Custom fit shelves that go from the perpendicular wall to the door trim would look great, but since the space is symmetrical, you could also just buy white shelving units and put them on either side of the door. They're usually only 12-15" deep, which I don't think would be too deep. The top of the shelves should be even with the top of the door if built-in and lower or the same height if stand alone. The wall space over the door in high ceilinged rooms is usually ignored these days because in general, a tendancy toward minimalism is more popular than a busy look. After you have shelves see how you feel about the empty space. You can always repost with an updated picture if it still bothers you.

Pictures of all 4 walls would be helpful along with a floor plan with dimensions, windows and doors marked. The room looks narrow so I would say no to any type of built ins.

It might be a good idea to look at some built-in options. Are you able to add more images of the room? They don't necessarily need to go all the way to the top of the wall. Here are just two ideas from a few designs below.

North Shore Family Home · More Info

Manhattan Contemporary · More Info

Would you be open to doing tall shelves or some type of built-in shelves. Here are a few of the designs we have done:

Issaquah Modern Family · More Info

Bellevue Penthouse · More Info