This begs the question of what a "real name" is. Many people use nicknames in place of their first name, and a majority of people know them by that nickname. Is a "real name" then your legal name? Where is the line?
This also begs the question of why a real name is required in the first place. If it's to thwart spammers or to assume people will be nicer if they have to have all posts show their real name, nothing is stopping anyone from saying they're "Joe Smith" and spamming comments, incoming streams, et al with their crap. After all, "Joe Smith" is a REAL NAME.
If it's to allow Google to better link your data, then having your real name public is not needed. Google can ask for this as private data and still be able to do it's big data crunching. Requiring it just asks for people to put in fake (but real sounding) names to get around it which ends up poisoning Google's data well anyway.
I frankly can't think of any reason why it should be required.