Elizabeth Fritzl rejected the offer by the government to issue new identity for her family.
She would probably just change the Surname to start her new life after she leaves the clinic in this coming December after her father's trial. They will be moving to a place about an hour from the dungeon house where she was locked for 24 years.
She has been trying very hard to help her children to live a normal life. She teaches her children how to play as Stefan and Kerstin has never gone out of the dungeon all of their life until this incest case surfaced in Apr 08.