They talk about having a document, presumably by a respectable third party, with that name. I guess for 1337 names, having a conference invite under that name would count. Concert or stand-up flyers for a persona would make sense. I'm less sure about how to have street names written.

In middle school, a student's nickname was “Simpson”; it's hard to explain, but he genuinely looked like he had yellow skin, expression-less face and spiky hair. In a court yard of a hundred student, everyone knew instantly which kid was ‘Simpson’. No one knew his actual name. When he was part of a group of kids who attacked me, it felt really odd to make a report listing his name, even after the headmaster had shown me on the photobook that that was his civil name. I don't remember if his nickname appeared on the report, but I guess any documented evidence like that would work.