When you say you have 100% custody of the children, this is only half true. The kids may spend the majority of their time in your care, but in terms of major long-term decisions, you share equal parental responsibility with the father, which means there are no options for amending the children's name without his consent, or by order of the court.
The first step is organising a family dispute resolution conference to try and reach agreement with the other parent about this matter. If agreement can't be reached, then you will be issued a s60I certificate, which will enable you to pursue parenting orders through the court.
The Family Law Act 1975 stipulates that all parenting orders (which also includes changes of name) must be made in the best interests of the child, which is guided by section 60CC of the Family Law Act, but there is a sort of 'added list' of considerations when it comes to changing a child's name. These include (but are not limited to) the effect on the child of the name being changed, any embarrassment they might feel about having a different surname to other members in their family, and the impact of the name change on the child's relationship with the other parent.
In any case, you must first attempt family dispute resolution with the father before court proceedings can be pursued. I hope this helps.
