A bit off-topic, but now you don't have to follow the G+ name rules if you're famous enough. At least if "famous enough" means "being Madonna". [1]
I don't remember her last name, but I'm pretty sure it is not ".".
I don't remember her last name, but I'm pretty sure it is not ".".
"we need to verify that your identity matches the one on the profile"
That doesn't necessarily mean that the profile has your [full] legal name attached to it just that it is properly associated with you. YMMV and probably will.
As lots of people have proven already, this doesn't work. There were suspensions of people that went by their 'commonly used name'. Lots of people still cannot use their 'commonly used name' because Google likes to play the 'I don't believe that you provide a common name for you. Prove it!' card.
'Commonly known' is totally undefined and the process to 'verify' this fact (why? why?) is undefined as well. So the whole rule is - bull..
As someone else said it: It's really just a 'give us the name on your passport' rule, with exceptions for celebrities and some very vocal/prominent/supported few.
And of course, being banned from G+ for using your real name is one thing, but it also partially or completely lock you out of other, unrelated Google services (Reader, Picasa, Data Liberation, your Google profile, potentially GMail and Google Chat). G+ is a death trap.
[0] http://infotrope.net/2011/07/22/ive-been-suspended-from-goog...
[1] http://infotrope.net/2011/07/25/preliminary-results-of-my-su...
[2] http://www.docpop.org/2011/08/googles-antisocial-behavior/