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.
The significance could vary greatly. It might be a creative concept for a story, perhaps about a character getting a new name and embarking on an unending adventure. It could also be a metaphor for new beginnings that seem to have no end in terms of the possibilities and experiences that follow.
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.