Because Alexandra created sci-hub to open access to science. It was a political act. She was not ashamed, she wanted people to pay attention. Perhaps she was naive in thinking that removing barriers to science and knowledge would trump middle-men's greed and profit.

Was her identity well-known before the Elsevier court case, where she was named?

I thought the publicity for her efforts was made after this, in English language media anyway. Though perhaps I am misremembering the order of events.