Google (used to) have a controversial strict "real name" policy on G+ and even very aggressively shut down accounts that had "fake looking" names, despite these people having said names. It discriminated against people who had (legal) Mononyms (single name) which is actually common in some cultures. They also didn't allow "unusual characters" in names. They asked for proof of name for shut down accounts and sometimes that proof wasn't good enough for them.

More info here including the weird things that triggered the auto flagging of profiles, and what shut down accounts couldn't do:

http://infotrope.net/2011/08/04/google-plus-names-policy-exp...

From the link above:

If you change your profile name, the following things seem to trigger the automatic flagging system:

    Mononymity, i.e. having only one name (and having just a dot, or similar, in the “last name” field).
    “Unusual characters”
        Actually unusual characters, like a heart symbol (❤).
        Punctuation marks, including quotation marks, parentheses, and possibly even hyphens and apostrophes. 
    Unusual capitalisation (including capitals appearing within a name, as in McWhatever)
    Spaces in either part of your name, for instance “Marie Claire” as a first name.
    Name using more than one character set, such as a name which uses the Latin character set for their first name and the Chinese character set for their last name.
    Certain words, possibly including profanity, names of famous figures or deities, etc.
    Professional titles such as Dr., Prof., etc.
    Suffixes such as III or Jr. 

The above is an incomplete list.

This is beyond bizarre because there are all kinds of names with those attributes, especially "unusual characters," (hyphens and apostrophes, periods) spacing, many first names, many last names, letters, "profanity," deities.

There were reports of people who have "two first names" as legal name (example Ron Paul, and the fictional Gwen Stacy) being suspended without warning as a violation of the real name policy.

They seem to have relaxed that policy some. They got a lot of backlash because of the policy and especially their strict policing of it and blanket suspension without warning of "offenders."

https://support.google.com/plus/answer/1228271?hl=en

Google+ makes connecting with people on the web more like connecting with people in the real world. It's recommended that you go by your first and last name because it will help you connect with people you know and help them find you.