The baby died in Kaitaia two years ago, and the coroner's report last week warned about drinking alcohol while breastfeeding.
The two-month-old girl, who was born prematurely to a Northland family of seven, had a blood-alcohol level six times the legal driving limit for an adult.
Family spokesperson Teresa Tua said the publication of the baby's name had hurt her brothers and sisters.
"Those kids read the comments on Facebook, they read about their mother and the coroner's findings. They were like, 'they're saying this stuff about my mum'.
"The kids are at school and they're getting told 'your mother's a murderer'. They ended up having a fight at school over it."
The children's grandmother, who is their caregiver, has also been on the receiving end of abuse about her daughter, Ms Tua said.
The publicity had been devastating for the whānau, and they should have had a chance to ask for name suppression before the coroner's findings were publicly released she believed.
Coronial staff have apologised for forgetting to notify the baby's grandmother before the report came out.
They said the report was sent to the baby's mother and father at separate addresses, but the father's letter came back unclaimed.
Mrs Tua said the mother did not receive the report.
"They knew the nana was the caregiver, she was the main person in this to be notified and they had her phone number and address - and she wasn't given a chance to comment."
The family was looking at their legal options, but could not afford a lawyer, Ms Tua said.
Coronial staff said because the case was officially closed the coroner could not offer further comment.