Ever since it launched, Google+ has been criticized for strictly enforcing a real name policy. You couldn't just use your gamer tag or other name you would use to signify your online or offline identity. Instead, you had to use your real name to use the service (though you could obviously just make one up of you felt like doing so). Today, Google announced that it's naming policy was going to become more "inclusive," but that doesn't mean you can now just become CmdrBurrito on Google+ because you felt so today.
Show Me Your Papers
Instead, the only way to use a real pseudonym is by more or less applying to Google to use one. This means that you will have to send some extra information to Google to confirm your established online identity. You can't just establish a new one on Google+.
Among these possible proofs of an established identity are "references to an established identity offline in print media, news articles, etc," "scanned official documentation, such as a driver’s license" and/or "proof of an established identity online with a meaningful following." What exactly constitutes a "meaningful following," of course, remains undefined.
For Google, being more inclusive then mostly means the ability to add a nickname to your profile, though your full name will continue to appear with your posts (think John "Hammer" Smith). You can't just go by your nickname. This should make things a bit easier for users with very common names.
Also new is support for using scripts outside of the regular Latin alphabet, so your name could now be सौरभ शर्मा (Saurabh Sharma).
Google Doesn't "Give a Damn" if You Use Your Real Name
The fun part of all of this is that Google doesn't really care about your real name either, of course. As Google+'s chief architect Yonatan Zunger points out in a comment on today's announcement, "name check is therefore looking, not for things that don’t look like “your” name, but for things which don’t look like names, period. In fact, we do not give a damn whether the name posted is “your” name or not: we will not challenge you on this basis, nor is there any mechanism for other users to cause you to be challenged for this."
Keeping the Google+ Community Clean
As I wrote in the early days of Google+, the service is somewhat akin to a planned community where Google plays the role of the Home Owners Association (HOA). This is not the chaotic environment of an accidental success like Twitter. This has its positive and negative sides, though it's obviously Google's community to run and those who move into a neighborhood with an HOA know what they are getting into.