I notice that for several games on Kongregate, the copyright notice either uses the author's handle name (login name), the name of the group that produce it or a domain name.
Are all those valid copyright notices?
That probably depends upon the court, and in some countries to a great deal on how well the lawyers fight.
In any case, do remember, copyright applies no matter such notices. They may make claiming damages easier, but a missing notice is in no way a carte blanche for copyright infringement.
In general, your copyright notice should be either using your name or the name of your company. If the name of your company happens to include the TLD of your website, so be it.
Yes, I'd say they're valid copyright notices. IANAL but in the US works under a pseudoname are just as copyrighted as they would be under a legal name, however they'd have to be able to prove that you're 'insertnamehere'.
Kongregate only attributes them that way because they don't require more information and I wouldn't recommend doing it for your own project.
As a general rule I think a copyright notice would have to identify the legal name of the owner ... your name, your company's registered name, etc. if for no other reason than to be able to look it up in the event of a dispute.
It is possible that a domain name may be appropriate (since they're registered), but a handle or other alias probably isn't valid (after all, you'd have to prove that you are the person the handle identifies).
It will depend upon the country where the copyright is held, and generally you dont have to file it anywhere. You should look into the jurisdiction where the website is located/hosted.
If it is US based the copyright standards dont require it to be their given name, only something that connects the authors identity to the material work they are presenting. That could be their email, login, company name, domain, logo etc.