Final answer:
The serving vessel made of Sue ware or Sueki stoneware with ash glaze used during the Kofun period is referred to as Sue ware.
Step-by-step explanation:
The vessel used during the 6th century Kofun period, made of Sue ware or Sueki stoneware with ash glaze, is referred to as Sue ware. Sue ware was born out of the advent of new pottery techniques during the Kofun period in Japan. This type of pottery is characterized by its grayish color and was typically used for cooking and storage. It reflects a significant technological advance in Japanese ceramics, benefitting from the local production of iron tools and immigration of skilled artisans, as observed in areas such as the Kibi region.