I've been less visible on this subject than others, due to time constraints.
I happen to use my real name in my Google Profile, which, funnily, isn't[*]. In part, because I never planned to do anything with my Gmail account. But then I wound up using it for work, and then someone sent me a G+ invite, and I felt obligated to give it a try. So, it's mere coincidence that I actually conform (apparently) with the G+ community standards for naming, or whatever it is.
Skud has been great as the go-to person on this subject. Check out Google+ names policy, explained
The whole 'give us a government issued id with your name on it' thing from Google is quite creepy, aside from the issues of one's commonly-used names and one's i.d. not always matching and how being asked to use your 'real name' on your profile is problematic for minority communities (trans, women, etc), as so many have written so eloquently already.
They're asking you to scan a copy of your government issued i.d. and email it to them. What?
This insistence on a government issued ID that they claim will be deleted immediately causes a situation rife with the possibility of identity theft, doesn't it? I mean, come on, how many reading this work in IT, or used to? We all know how easy it is for things NOT to be deleted. Backups, rollbacks, cron jobs that don't work right, and the ever-popular "I'll get to it eventually."
I'll be on Diaspora, instead. http://joindiaspora.com
[*] Isn't my real name. Except when it is. Like, on most of my government IDs. It's just not the name on my birth certificate, which is also a government ID. Why? Because my mother remarried when we were 8 or 9. And it caused a whole big drama when I tried in my 20s to get a passport in what I *thought* was my name, but is actually an alias, let me tell you. Holy crap. So, dear Google, I've been using a pseudonym almost my entire life. Which name *should* I give you, really?