As far as I know, no. The princess in 'The Neverending Story' is often referred to as Princess Moon Child, and I haven't heard of any new name being given to her.
I'm not sure specifically which new name for a princess in 'The Neverending Story'. There are various versions and interpretations, and without more context, it's difficult to give a definite answer.
Princess New Name in 'The Neverending Story' was often seen in the enchanted forest that was at the heart of the story's world. This forest was filled with ancient trees that could talk and magical animals. The princess had a close relationship with these forest dwellers. They would often give her advice and help her when she was in trouble. One of the most memorable adventures she had was when she had to cross a river made of stardust. With the help of a friendly unicorn, she managed to do it and continued her quest to bring peace and harmony back to the world of 'The Neverending Story'.
Well, the name of the princess in The Neverending Story is Moon Child. She plays a significant role in the story. The story is filled with all kinds of fantastical elements and she is sort of like a symbol of hope and beauty within that magical world. The protagonist Atreyu has to go through many challenges to reach her. And her presence is what kind of drives the plot forward in a way as Atreyu's journey is all about getting to her and saving her world from the Nothing.