The birth certificate registration only has information about the child's date and place of birth, and who the parents are. If you choose not to put the other parent's name on the birth certificate, that parent's legal relationship to the child is still the same, including their obligations to pay child support and their right to ask for:
- parenting time and parental responsibilities under the Family Law Act,
- parenting time and decision-making responsibility under the Divorce Act, or
- contact with the child.
It's a good idea to get legal advice about this. See Tips about getting legal help for where to find a lawyer.