Consecutive heads of the Ura-senke school have inherited the name "Soshitsu," which was the real personal name of Senso the 4th head of the school, but unlike the Omote-senke and Mushanokoji-senke schools, this school doesn't seem to have had a tradition of the current head inheriting the name of his predecessor during its early years or of the Wakasosho (the koshi, or successor, to the current head) assuming a special name.
裏千家の家元は四代である仙叟の諱「宗室」を受け継いでいるが、表千家・武者小路千家とは異なり初期は襲名をしていなかったらしく、また家元後嗣（若宗匠）が特定の名を名乗る伝統もない。