I'm fascinated by the assumption that a name change is done mainly out of spite. Oh, and only the heritage of the father's family and identity matter. Hmm. Nothing at all to do with a mother wanting to have a connection to their own child with their name? You know, the thing that so many fathers scream blue murder about if the suggestion is made to change said child's name. 
I have my DD registered at school, doctor, dentist etc. with my surname, despite having her dad's surname on her BC and passport. Nothing to do with spite whatsoever. All to do with wanting to have the same surname as my DD (seeing as we are a family, ex barely registers) and not having to continually explain who I am to people I deal with over issues concerning my DD because we don't have the same surname. I never wanted to have a different surname, it meant something to me before she was born but I was 'persuaded' to give her, her dad's surname as we were supposed to be getting married. So, we'd all have the same surname anyway. I was pretty much brow-beaten into agreeing to this, even though it never has sat well with me - when you are faced with the father of your child threatening to leave over something that seems insignifcant in the overall scheme of things, you can end up agreeing to something that never sits well with you. All the appointments with HV, MW, doctor, hospital, dentist etc. were done by me, and each and every time, I'm asked who I am because we don't share the same name. Given that I am the one raising my DD, I find that irksome to say the least. My family are the ones who actively contribute to raising DD, if 'identity and heritage' are important factors for a child with reference to their surname, then my family's identity and heritage are far more significant and important in the overall scheme of things. I would never dismiss my ex's family, heritage or identity to my DD, but the argument about the surname having such significance that only a father's identity and heritage has any significance really irritates me.
I've never had to justify to anyone my reasons for changing my DD's surname unofficially. Not once have I been asked to produce any of the evidence referred to in this thread. If doing this is illegal as has been said, and it was such a terrible crime, I do wonder why not one person I dealt with has ever challenged me, or demanded the documents/evidence to 'allow' me to do this. I did speak to my ex about this, and he had no objections, because he understood my reasons for wanting to do this - he wasn't prepared to do any of the hard work involved in raising DD, and accepted that it was 'irksome' having to either explain who I am in relation to DD, or to be continually mistaken for being mrs x-surname because of my DD's surname. He still feels strongly about DD having his surname, and that's the reason her BC and Passport remain unchanged - it's a compromise that he has accepted, and tbh, if he didn't, then that would be 'tough'. I'm not spending the rest of DD's childhood having to explain myself, who I am, simply because society deems it more important that a mostly absent parent have their 'identity and heritage' protected at all costs.