Advice from the former chief prosecutor, Nazir Afzal who wrote on Twitter, If you name someone and get it wrong then they may sue you for defamation and you can say goodbye to everything you own. So don't.
If the mother felt that the BBC were unreasonably dragging their feet over the investigation, I believe it would have been better to contact the Police - or even her MP. Going to The Sun was a bad choice. Her child, though not named, and no longer a child, will be having a tough time over this. As will all those innocent news presenters who now feel compelled to declare their innocence.
This is all so wrong on many levels.