The name of the tea house inside Kenrokuen where we had the tea ceremony is Yugao-tei Tea House.
I was right when I guessed earlier that it wasn't a tea house. It was actually a rest house, which I suppose is a house where people rested.
This series of photos was taken in one of the smaller rooms of the tea house. We were alone, so I promise that we didn't bother anybody when we took these pictures.