How can I decorate with a single white shutter?

One option is to make a mail organizer. You could chalk paint it nicely and then use it for that practical purpose. Here is one: https://www.hometalk.com/diy/organize/storage-ideas/shutter-the-clutter-26435554

My husband made a canning cupboard some years ago. He used antique shutters for the doors on it. I have hung thin med. sized s hooks on the levers in different spots and hang some of our larger kitchen utensils on it that do not fit in drawers well.

You can hang in in your entryway and turn it into a key hanger. Add some trimming around it and connect hooks to hang your keys.

I saw one years ago with phone numbers it hanging next to a phone. If the shutters work, you could put phone numbers on each side and use it next to your desk.

i use one with the slats for mail product different size envelope my roll of stamps next to my desk on the wall