Also, what exactly do you mean by "people" didn't know her name? She knew it. Presumably people close to her - her two brothers if no one else - knew it. And in the interrogation here it's never a question of anyone but her giving her name. It's clear that she had been calling herself by her mother's maiden name to escape notice but that she was denounced by someone who recognized her as Robespierre's sister (whether or not he knew her name was Charlotte is immaterial) at which point she saw no point in denying her identity any longer and provided her given names herself. No one else needed to be aware of her given names for her to confirm them.