One identity that was mentioned was as Dutta's dark-skinned friend Naku. That, because of Babi's actions, Naku defines herself and sees herself only as the dark-skinned, not pretty girl, a koyal. That this is all she is or allowed to be
The other identity is Naku the girl with her own world view, her own standards, values...the identity independent of Babi, Dutta. Her strength, faith in herself.
I don't think what is keeping her from telling the truth is that she sees herself as Dutta's dark-skinned Naku. That that is how she defines herself and wants to be. I would hope she hasn't lost her own identity.
I think plain and simple that it is a fear of his reaction that keeps her from telling the truth, and not this Naku vs Naku conflict within herself. Naku knows damn well that Dutta is close to her because of herself as a person. Yes, he has a problem with beauty. But does she really think he will hate her for her beauty or her lies?
What do you think?