I would have thought that the registrar would have to abide by a court order, but I'm by no means certain of this. Might be worth having a word with the Scottish Child Law Centre on this.
Not sure about in Scotland but I spoke with the General Register Office for England and Wales. Although PR has been given at court, we were told that anybody can be given PR, so we need a specific document before they will add the fathers name to the birth certificate unless the mother signs the form to say it can be added. If the mother will not do this, you need to get from court:
Parental Responsibility Order
Under Section 4
Children Act 1989
Was told very specifically that it has to be this and nothing else. Once this is obtained, a fathers name can be added without the mothers consent.