[Blomkvist] had come to realize she was a world class hacker, and within an exclusive international community devoted to computer crime at the highest level – and not only to combating it – she was a legend. (1.24)
Blomkvist, crime fighter that he is, obviously admires this aspect of Salander's identity. She, on the other hand, sees nothing special in it and doesn't seem particularly proud of it.
[Salander] had spent five weeks in a clinic outside Genoa getting the implants that formed the structure of her new breasts. (1.53)
Even though Salander might seem highly confident in a fight, on an investigation, or at a keyboard, her body is a constant source of shame to her. The breast implants do seem to help this, but her feelings of low worth go deeper than skin.
Every day [Nils Bjurman] was confronted by the tattoo on his body. Finally he took down the mirror from the bathroom door. (2.16)
After Bjurman rapes Salander, she tattoos his identity as a sadistic rapist on his body. This forces him constantly face the fact that he's the sort of person capable of this kind of terrible action.
She lacked social inhibitions, one of her reports stated. Well, [Bjurman] could conclude a stage or two further: she was a sick, murderous, insane f***ing person. A loose cannon. A whore. (2.102)
Bjurman is reading the social welfare reports on Salander. These show how she's been identified by the system. His thoughts show us what her identity is in his mind.
Her eyes filled with tears. Never in her life had she felt like such a selfish s***. And never had she been savaged in such a furious manner. She bowed her head. (8.37)
Armansky has just let Salander have it for being so careless with those who care for her. But what she's upset about is assuming her beloved guardian Holger Palmgren is dead. Palmgren is one person who she knows cares about her. Now that she knows he's alive, her identity as his friend can return.
Armansky: "Files are one thing. People are something else." (13.180)
Armansky is trying to explain to Bublanski that you probably can't know a person by reading a file on them. You can only really know a person by getting to know them.
Blomkvist: "She is a very lonely and odd person […]. Socially introverted. Doesn't like talking about herself. At the same time she is a person with a strong will. She has morals." (14.156)
Would Salander agree with Blomkvist's assessment of her identity? He seems pretty spot on, illustrating her seemingly incongruous strengths and weaknesses.
The letters were irregular and clumsy […]: I AM A SADISTIC PIG, A PERVERT, AND A RAPIST. (15.146)
This is where the police see Bjurman's tattoo after he's dead. The tattoo leads them to believe that, like Salander, there's more to his identity than what's on public record.
Modig: "So you don't actually know if she's sick or not […]. I mean, if there wasn't any diagnosis." (17.142)
Inspector Modig is challenging Salander's ex-psychiatrist Peter Teleborian. She recognizes instantly that Salander's diagnoses are based on the fact that she wouldn't allow herself to be assessed.
Despite her years of striving for anonymity, she had been transformed overnight into one of the most notorious and talked about individuals in Sweden. (21.3)
Watching how the media constructs an identity for Salander with no basis makes us wonder if we can trust anything we read or hear in the media.
As she fingered the hole in her skull she realized she was touching her own brain, that she was so seriously wounded she was dying or maybe should already be dead. (32.117)
Salander is on the verge of totally losing her identity, at least as a living, breathing human being. Luckily, Blomkvist isn't about to let that happen.