If a skeleton is carrying a named bow in their offhand and they kill a player with it the death note shows the item in the skeleton's main hand (If the item in its mainhand is named).
E.g if a skeleton is holding a sword named sword in their mainhand and a bow named bow in their offhand and they kill a player using the bow the death note says something like: "Player was shot by skeleton using [Sword]", instead it should say: "Player was shot be skeleton using [Bow]"