The Handmaid's Tale
How we cite our quotes:
Falling in love. [...] It was the central thing; it was the way you understood yourself; if it never happened to you, not ever, you would be like a mutant, a creature from outer space. Everyone knew that. (35.13)
While in Gilead it's dangerous to try to remain yourself in any form, in the time before that people believed that "falling in love" was a crucial part of forming one's identity. Now that seems like a luxury that Handmaids living in this new reality can't afford.
I have been obliterated for her. I am only a shadow now, far back behind the glib shiny surface of this photograph. A shadow of a shadow, as dead mothers become. You can see it in her eyes: I am not there. (35.35)
The narrator was robbed of her identity as a mother when her child was taken away, but that didn't mean she didn't feel like a mother any more. This is a second theft of her maternal identity, when she realizes her daughter no longer remembers her. This makes her feel like she doesn't even exist.
I tell him my real name, and feel that therefore I am known. I act like a dunce. I should know better. I make of him an idol, a cardboard cutout. (41.19)
Here the narrator explicitly connects the power of her "real name" with being known and understood. This calls on the fairy tale trope of a name-giving power, like how Rumpelstiltskin's name is the answer to his riddle. And in fact, admission of the narrator's name to Nick does give him power over her.