The problem of bullying on the Internet is in many ways related to the problem of anonymity. Anyone can insult another person without being recognized and, therefore, without fear of punishment. Children are most vulnerable to such kind of bullying since they are unable to defend themselves psychologically. This study is devoted to cyberbullying among school students. The phenomenon of cyberbullying in this study is divided into situations inside and outside the school community. As for school cyberbullying, it is basically offline bullying continuing online. The victim and the persecutor personally know each other. Anonymity can be achieved by using fake accounts. In non-school cyberbullying, the victim and the persecutor are unfamiliar with each other in real life. Potentially, a student may be the victim or the persecutor. They may also be a witness to online bullying. The purpose of this study is to analyze the relationship between open (non-anonymous) bullying on the Internet and bullying using fake accounts which provide a sense of anonymity and impunity. Totally 1762 school students of the Sverdlovsk region took part in the study. For the purposes of this study, a questionnaire on cyberbullying inside and outside the school community was developed. The hypotheses of this study are the following: (1) In school cyberbullying, bullying using fake accounts will occur more often than open bullying under a real name or main account. (2) In non-school cyberbullying, bullying using fake accounts will occur with the same frequency as open cyberbullying under a real name or main account. The results refute the first hypothesis and confirm the second. When cyberbullying occurs inside the school community, open cyberbullying has an advantage over hiding “behind the mask” and using fake accounts. In non-school cyberbullying, bullying using fake accounts occurs with a comparable frequency to open cyberbullying.