About Princess of Han 漢宗女
A member of the Imperial family (surname 劉 Liu), it is not recorded (and forever unknown) who her parents were. In many unfounded online sources, the father was given as "Hui", perhaps referring to Emperor Hui of Han.
The original source is Sima Qian's "Historical Rrecords", and the "History of (Former) Han" contains a nearly identical passage, but with the altered word 翁主, perhaps a mis-copy of 公主 (Princess).
"後頃之，冒頓死，子稽粥立，號曰老上單于。老上稽粥單于初立，文帝復遣宗人女翁主為單于閼氏，使宦者燕人中行說傅翁主。說不欲行，漢強使之。.... " --- 《漢書》
"... Shortly after this, Maodun died and his son Jizhu was set up with the title of Old Shanyu. When Jizhu became Shanyu [in 174 BCE], Emperor Wen sent a princess of the imperial family to be his consort, dispatching a eunuch from Yan named Zhonghang Yue to accompany her as her tutor." --- Sima Qian: Historical Records (tr. Burton Watson)