Regardless of the mother abandoning the child, the fact remains that you know the child mother's name and that should be on the birth certificate. The Canadian authorities will be interested in knowing about her so you cannot run away from that. They will also need some form of documentation from either the court giving you legal custody of the child. However, I am no lawyer and you can double check on that last point.
The child will have to be in Canada and get PR status, but those issues mentioned above will have to be address first.
The child will have to be in Canada and get PR status, but those issues mentioned above will have to be address first.