I'm no expert on the Meiji era, but based on some googling I did, it looks like Teru is Matsudaira Teru, an aristocrat who helped defend a castle during the Boshin war, and her brother, Matsudaira Katamori, was an important Daimyo. Her refusing to share her brother's name made me think that they were on the imperial side, but both brother and sister were on the side of the shogunate, like the Shinsengumi, so I guess she was just trying to hide the fact that her brother was famous.