字 [あざな] azana, a formal nickname. For example, "Shoukei" is an azana. Her given name is Shou, which she never uses in public. Keikei is a child's nickname (小字).
数え年 [かぞえどし] kazoe-doshi, lit. "counting years"; the old manner of reckoning one's age, newborns being considered a year old, with everyone adding one year to their age at the New Year.
柳国 [りゅうこく] Kingdom of Ryuu (lit. "willow")
和州 [わしゅう] Wa Province
拓峰 [たくほう] Takuhou
蘇 [そ] So, Rangyoku's family name