Her full name is Hata no Kokoro, with Hata as the surname and Kokoro as the given name. Hata (the Japanese reading of Chinese surname 秦) clan was an eminent Chinese immigrant clan mentioned in Nihon Shoki. It's also the surname of the masks' original user — Hata no Kawakatsu, who's said to be the reincarnation of First Emperor of Qin Dynasty in Zeami's Fuushika-den.
Her given name is written entirely in hiragana and means 'Heart' (心 kokoro) in Japanese. 心 is also in the Japanese title of the game about her: Hopeless Masquerade (心綺楼 shinkirou).