Is it legal for one parent to change a child's name on their Health Card without the other parent's consent.?

The parent's have joint custody and the child lives with the father in Quebec. The name that she was given at birth and what she was christened as but after the separation, without any consent whatsoever, the child came for her visit and the health card read a different name. He placed his last name in it. I.E. Her name is Ann May Hope and it now reads Ann May Ritney Hope. Could anyone give me any ideas on finding out if this is legal or fraud?