I think this is a complex question. The inference given is that he murdered her because he couldn't face that he'd raped her. This does happen. Some criminals are hardened or get off on their crimes, but others suffer PTSD at the acts they've committed and some DO enter a state of denial very deep and thorough in order not to recall/face up to what they did. If that is the case for him it's hard to know how he sees himself. He may have completely convinced himself it didn't happen and he didn't do it, in which case if he can maintain it i think he will want anonymity because it helps him maintain the veneer of being an innocent child now awaiting appeal for his miscarriage of justice.
On the other hand the innocence plea may just be part of an "i'm a good lad really" act he's putting on because he's a narcissist, all the while secretly enjoying the hurt he has inflicted (and plenty in the trial points to this just as much to him being in post traumatic denial), in which case he might enjoy the idea of notoriety.
It will make very little difference to his day to day life. Every member of staff involved with him and every prisoner he is in with will know who he is and what he's done no matter what the judge decides, and i doubt he is too concerned about what will happen to his relatives given he took the stand and said his mother is an alcoholic.