In Ibsen's A Doll's House, does Nora's name have any symbolic meaning in the play?
In the context of the origins of the name "Nora," several sources report that it is short for "Eleanora" meaning "light," and "Honora" meaning "honor."
I have not found anything to indicate that that the author purposefully chose this name for the protagonist. However, in Henrik Ibsen's play, A Doll's House, these meanings may be used to contemplate a deeper side of the character of Nora.
Nora can be seen as the light in several ways. It is Nora's bustling and energetic personality that brightens up the room upon her arrival in the opening scene. We see this when she is returning from Christmas shopping. Torvald also might, arguably, be drawn to the light in her: he would not refer to her in such childish terms (i.e., little bird, songbird) if she was something that was not bright and cheerful. Even the dying Dr. Rank is attracted to Nora, much like an moth to a flame. There is warmth and comfort to be found in her presence. When Nora leaves in the end, it is very much as if the light has gone out of the house and Torvald's life. He laments:
Empty. She is gone.
In terms of honor, we see clearly that Nora is an honorable woman. She took money illegally to save Torvald's life. She is extremely agitated when she believes that she might be a poor mother to her children because of this act. Nora is worthy in her respect of Dr. Rank's wish that he be left alone at the end to die. (Torvald, Rank's "best friend," secretly infers he has little regard for the other man.
[in a fretful whisper]. Oh, what does [Rank] want now? (Act III)
Rank knows death upsets Torvald and doesn't want him around, and Torvald agrees without hesitation.) Nora is noble with regard to her commitment to be a good wife, loving and caring for family even before her own good. She wants very much to protect Torvald from any repercussions based on her business dealings with Krogstad, even contemplating suicide, insisting to her husband:
Let me go. You shall not suffer for my sake. You shall not take it upon yourself. (Act III)
Finally, we might argue that Nora's decision to leave at the end is a exercise as she honors herself, and all that she can be.