I am writing in the context of Malaysian Birth Laws ONLY
In the birth certificate (for non-Muslims), the name of the mother must be inserted regardless of whether the mother is of Malaysian Nationality or not, by the presentation of maternity records from either Govt or Private Hospitals.
The name of the father is not compulsory if it has some restrictions by local laws.
The Citizenship of the child will follow the citizenship of the mother.
If the mother is of Malaysian Citizenship, the status of the mother documented inside the Birth Cert will be “Single Mother”. However the child will be deemed as an illegitimate child under Malaysian Non-Muslim context.
For Muslim mother, Islamic Laws do not recognize this child if born out of wedlock and will be seized by the religious enforcers to be put up for adoption.
To understand Laws on Nationally and Citizenship of Malaysia, please read under this link :
Citizenship and Nationality: What are "Stateless" and "Registration under Section 13" Children?