[Shujin]

But---Why don't you just swap accesory one with accesory two?

Item name has nothing to do with which slot they take? Or I also don't get what you mean.

You want to swap, just from a visual perspective in profile have the collar in slot 1 and cloak in slot 2?

Edit:
okay that was akward, I tested it with a couple of items,
I figured it out though for you. Its not the Name, its the Inventory order.

Do attempt, inside your inventroy to drag the Cloak below the collar, and try equipping them then. (Like the actual inventory under Equip tab)