iPhone X replacement

Nothing other than the phone. Any required diagnostic will be done via WiFi or maybe the Lightning port. They don't care about the box. A replacement typically comes in a white box without any graphics. There will be no accessories packaged with the replacement.

Make an appointment. These seem to be the two closest Apple Stores.

Reston - Apple Store - Apple

Fair Oaks - Apple Store - Apple

Where are you located?

No, they do not need the box.