As IM states, the birth certificate can't be changed under the circumstances you describe:
http://www.gro.gov.uk/gro/content/births/canic hangethebirthrecordatalaterdate/birth3c.asp
There's no reason why your grand-daughter can't simply be known by her mother's surname, for 'day to day' purposes. (When I was teaching, there were many children who were known, say, as Mary Jones while their birth certificate gave their name as Mary Smith). However, problems can arise with official paperwork. The one we always had to sort out was that GCSE examination candidates are meant to be entered for examinations under the name on their birth certificate, unless it's been formally changed as below. (Trying to explain to 'Mary Jones', and her family, that her exam certificates would be in a name that nobody had ever used for her could often be very difficult). As IM states, passport applications can present even greater difficulties.
The way round this is to change the child's name by a statutory declaration (which will satisfy bodies like school authorities but not the passport agency) or by deed poll (which satisfies all legal requirements). See here:
http://www.thompsons.law.co.uk/ltext/changing- your-childs-name.htm
Chris