Since you have an open door policy, you can have a little fun with it. Every time an employee comes in to speak with you, thank them loudly for stopping by and to please close the door. Have your little meeting and when they walk out loudly tell them to send in the next one. Then smile and go back about your work.
Well, I didn't say it was a good idea.
Seriously though, I would definitely close the door if it's noisy.
If you hide your deafness, then no one will bother to accommodate you. It should be a two way street and if you don't tell people then everything becomes a one way street. You decide what you need to do your job effectively.