Some great resource here on Children/Youth internet safety.
A few thoughts…
One stream of thought says to maintain internet safety by using a false name when making comments. As Donald Miller would suggest, the internet is the "Wild West" with few rules. The other stream of thought says that by hiding behind false names, people have more incentive to say/do things cruel/offensive without having to take responsibility.
I don't think kids need to be online at all for any length of time, other than perhaps learning research in their schooling. Gaming is a parental choice, I understand, but social networking is definitely unnecessary for kids. Teens don't "need" cell phones, and there doesn't seem to be an abitrary age at which youth are able to handle social networking. Like getting a driver's license, parents need to judge whether or not their children are mature enough to handle online interaction.
When parents don't model good online behaviour, we have a problem.
People can be real jerks online. I'm of the mind that if you're going to say something online, have the guts to use your name. Own your words. Trolls may attack… you might be the troll… but not every person on the web is ready to hack your account.
Keep kids safe online. Learn good habits. Know what to look for if your kids are having trouble.
… be you. No silly monikers or avatars. Own your words. Part of kids staying safe in life is being able to trust the adults in their lives. When those adults argue, call names, threaten, taunt, demean or hurt… kids learn this easily and quickly. No responsiblity necessary.
However… that's just my opinion. I do understand others' points of view when they wish to retain anonymity, no matter what they're sharing or how.