Guardian issue.

Regulations permit providing the mother's name also.   A candidate may mention the name of the mother also.

What is the necessity to change the father's name. It is the wife who has divorced from the husband, not the children from the father. The status of the children vis-a-vis the father remains unchanged, for instance, the divorced wife is not the legal heir to the ex-husband but the children, notwithstanding the divorce of the parents, continues to be legal heirs of their father as well the mother.