At what moment in A Doll's House do you understand why it has been given its title?
The problem with this question is that having read, studied, taught and thought about this play for a long time, I am able to pick up references to the text that might suggest the central governing image of Nora as a doll in a doll's house much earlier than this reference is made explicit. Therefore, consider the following quote from Torvald at the beginning of the play:
That is like a woman! But seriously, Nora, you know what I think about that. No debt, no borrowing. There can be no freedom or beauty about a home life that depends on borrowing and debt. We two have kept bravely on the straight road so far, and we will go on the same way for the short time longer that there need be any struggle.
Torvald is treating his wife as if she were a child, and as it is clear Nora is the protagonist, it does not take much of a leap of imagination to look at the way that Torvald treats his wife to see his control and treatment of her is reminiscent of an adult with a child.
However, if we want to look at explicit references to dolls and doll houses, consider this quote from Act III when Nora finally confronts both herself and her husband:
But our home has been nothing but a playroom. I have been your doll-wife, just as at home I was papa's doll-child; and here the children have been my dolls. I thought it great fun when you played with me, just as they thought it great fun when I played with them. That is what our marriage has been, Torvald.
If there had been any doubt before, the room and the marriage of Torvald and Nora is explicitly compared to a doll's house and dolls. The unreality and illusory nature of Torvald and Nora's marriage and life is thus made explicit and the reference to the title is definitely explored.