the scientist injected her a different syringe than the one that would have killed her, saying "here's your memory back" (or something like that, the dose she took daily was supposed to prevent the memories from returning, with the leaks she sees here and there, I guess the syringe would just remove all the "fog" the daily doses put on her mind) Maybe you should put a "spoiler" warning on the topic?

I think the syringe was actually some sort of stimulant to counter the sedatives. When the doctor said "here's your memory back" she probably just meant the thing with the apartment name and number on it. But yea, basically not taking the "medicine" and seeing things that would trigger a memory is how she remembered her name.

She was constantly having 'glitches' where she would see things from her past. The medicine she took daily was supposed to keep her memories suppressed. Dr. Ouelet gave her a stimulant to wake her up. She also gave her the address of where she used to live. But even before she stopped taking the 'medicine' her brain was fighting it. So actually going back to the places she knew just helped.