The baby girl, currently in foster care, was taken from her parents when she was 31 days old after concerns about her safety.
The baby's welfare is now under the responsibility of Leeds City Council.
Details of the case have emerged in a ruling by Judge Patricia Lynch following a private family court hearing in Leeds.
The mother, who has not been identified, had given birth under a false name four months ago.
She did not register her daughter with a name during the 31 days the child was with her at home.
The judge ruled the mother had also tried to "conceal" the little girl's birth from social workers.
Once social workers were made aware of the birth, they registered the baby "just with her surname" and had chosen an "appropriate first name" for use on a day-to-day basis, reported Yorkshire Evening Post.
The baby girl was put into foster care during summer 2015.
In earlier family court proceedings for the same family, a judge concluded that the girl's father had sexually assaulted another child, according to Yorkshire Evening Post.
Judge Lynch therefore concluded the child would be at risk of "sexual harm" if she was to go back and live with her parents.
She concluded the youngster should be placed for adoption.
In May 2014, an Indian father and his wife living in Hertfordshire refused to name their child, reported the Telegraph.
The unnamed couple said the reason was because they were "anxious to have their child named according to Hindu tradition, which involves a temple ceremony, Namakarana, which only the parents, close family and friends can attend".
Because of previous convictions, social workers pressed to be present at this event, to which the father refused.
Judge Justice Parker ruled by not naming the child, it created a "high risk of emotional harm" in the future. The baby was sent for adoption.
A similar story emerged in April 2015, where two parents refused to name their baby "because of their beliefs".
They said because of what they believed in (which included the Bible and human rights law), "her life is private and no-one else has a right to know about their family or interfere with their lives", reported the MailOnline.
The eight-month-old baby was similarly referred to by her surname by social workers.
However in this instance, the judge ruled the family should not be broken up, adding: "I am personally unconvinced that failing to name the child constitutes significant harm".