No problem. I don't check Medium that often but please do! I guess it does also depend on what you think identity is or means. Does changing the person named with your parental rights/responsibilities mean that you are a different person legally? And even if it does, what exactly does that mean in reality? Does that mean you are no longer you? I guess in the past those questions were not really talked about, but it is very much part of the conversation now, if not so much with adopters then definitely with step-parents, as there are millions of them. I think most people would say that you are still you, regardless of your parents! But trust me, adopters are definitely told that we must respect our child's 'identity'. We get an adoption certificate (eventually), but that isn't really used for much other than a nice piece of paper to put on the wall, if that's what you'd like. Passport records etc are checked against birth records, in the child's original family name.
Now if you want something to really worry about it is Parental Orders - mostly used in surrogacy and donation scenarios but not exclusively, where the original birth identity does not reflect any part of the gestation. It completely wipes from legal history something pretty important, i.e. your experiences in the womb.