I really don't think that painting all four walls would be too much. 2 walls might look odd

Agree with those that say paint all four walls navy. Your white ceiling and white door and window trim will be enough white against the navy so consider painting your white bookcase a pale blue.

Add brass or gold lamps gold or green or red throw.

One caveat: How much natural light will this room have?

If you have only one window that gets little if any natural sunlight, consider painting only one wall navy -- perhaps the wall with the window -- navy instead of painting two or more walls navy.

Then make choosing your light fixture more about it providing light than being trendy.

Paint four walls or forget it. It's one room, ONE color. Whatever the color. Don't be afraid of the navy, you'll be surprised when it actually appears a brighter room with white trim

Either paint all 4 walls navy or paint the ceiling navy. Make sure you repeat navy accents in other rooms in the house.

You can have 4 navy walls without having a light-sucking dark blue box.

Many years ago, I lived in a mid-century modern house with a study.

The wainscoting, built-in desk, bookshelves, and window seat were maple, and I replaced the dusty dated old pink and grey wallpaper with a dark navy wallpaper with a tiny white pin dot.

It was gorgeous.

Today you might want white instead of maple...