Means favored. Each generation of Tea Masters has many different Konomi, a partial list can be found under:
Maru-Joku - Round paulownia wood tana with two shelves, and a third leg in the back
Sanju-dana - Square paulownia wood tana with for shelves
Maru-Joku - Round Ikkanbari (black lacquer) tana with two shelves
Koko-dana - Square tana with three shelves. Either black lacquer with red edges on the shelves or paulownia wood.