I've tried changing the name a few times, I started the game again, but Anon always appears in emails and other things, I couldn't find where to change the nickname. Is there any option to enter the nickname?

Well, because that's how is supposed to be. As far as I'm concerned you can't change it. Maybe if you mess with the files but that obviously is not a conventional way. In a future update we might be able to choose the name who knows, although haven't seen anyone care about it. There's also a dialogue that makes a joke about his name, so it would get ruined if you could change it