As teachers, parents or edu-business owners ourselves, we're extremely conscious of child safety so we take all concerns seriously, but the short answer is yes, it's safe.
Here's a longer answer in three parts!
The only external-facing place where a real name could be displayed is at the end of a Festival or Arena game. Just because the real name appears at the end of a Festival or Arena game doesn't immediately pose a risk. After all, apart from the name there's no way to identify which school they're from or where they are in the world. Literally no way. So they could be John Smith, for example, from anywhere.
Furthermore, that real name is only visible to the few people who happened to be in the same game at the same time. Not strangers wandering past the website, not even kids playing in another game even if they're sat side by side. Just the ones in the same game who have to login to even be there.
Teachers can display rock names instead of real names at the end of a game by changing the first setting on Settings & Admin > Privacy Settings.
