At the birth of a child the parents can put their names on the birth certificate, and the name of a parent who is not present, the father in this case, could have been included on the certificate, as well, and it would have required no additional fee. To change a certificate after the fact there is some administrative requirements and as a result there is a fee, but I would strongly encourage parents to get their names on their certificates when they first fill out their application, both mother and father.
Glen Abernethy on Question 565-17(5): Birth Registration Policies
In the Legislative Assembly on February 6th, 2015. See this statement in context.
Question 565-17(5): Birth Registration Policies
Oral Questions
February 5th, 2015
See context to find out what was said next.