One could consider Princess Eilonwy from 'The Chronicles of Prydain' series. These stories have a rich, magical world much like 'The Neverending Story'. Eilonwy is a princess with her own set of skills and adventures. She is young and has to face various challenges in her world. For example, she has to deal with dark magic and various creatures, and her character grows throughout the series.
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.
I'm not sure if there is a princess named 'name' in 'The Neverending Story'. It could be a very specific or perhaps a made - up reference within a particular context.