We have an adopted son and he carries his certificate with him as when he was working through agencies they quite often asked for it. In the end we had to order a new cert for him as the other one was worn out, but I'm sure it states we are his adoptive parents on it. In fact one agency wouldn't accept it as they said it wasn't a "real" birth certificate. I told our son to go back to the agency and tell them that if the DVLA and other government departments accepted it, then so should their agency. He's never wanted his original birth certificate and in any case that would have a different name on it and wouldn't be proof of who he is.