Keeping in mind that I am in the UK, can anyone offer some advice.

A friend asked me to see if anyone can help with this problem. She and her partner split up after having a child together. The child had her father's surname but after a year of no contact with him the mother decided to change her daughter's name to her own. This was never officially done but registered with school and doctors and has been known by this surname for 15 years. Her daughter is now 16 and whenever any documentation is filled in everyone requests proof of name change. Of course, the daughter's birth certificate has her official name on but other documentation has the mother's name but no official documentation with name change on. Would it be best for my friend's daughter to change her name by deed poll now because she has no proof of the name change other than school stuff, national insurance card. She need to open a bank account for her daughter now but needs advice first. Thanks in advance and hope that wasn't too confusing.