Hi, thank you for your question. Just a bit more information required to fully assist you:
-Are you in England or Wales?
-How old is the child?
-Is the father named on the birth certificate or were they married?
As they are in Scotland, Scottish law takes effect and therefore I will opt out and allow a Scots Law colleague to assist.
Thank you for your question. Here is a link that will help you: http://www.nrscotland.gov.uk/registration/recording-change-of-forename-and-surname-in-scotland. A child over 16 can apply for a change of name. A child under 16 has to do so through its parent or parents with parental responsibilities. So if your daughter's residence order removed parental responsibilities she can apply for the change of name. If it did not then she either needs the father's consent or she will have to return to court to get an order removing his parental responsibilities. Alternatively she can just advise the school etc that the children are to be known with her surname which might be easier in the shorter term. Happy to discuss further. Please leave a positive rating so that I am credited for my time.