Google + name different than Website earnings name.

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I have ran into an interesting issue I am concerned about. now that Google + has come around, I have created an account in hopes to network and take advantage of the social media aspect of earning money online. I just simply used my pre-existing Gmail account. Now here is where i Run into a possible issue. I use this same email for many of the sites I use to earn money online. All the personal info I use to sign up is 100% accurate as should be according to most TOS, on each of the sites. But my Google + name I choose to use fake name for the simple reason that I Don't feel it is necessary to disclose all my personal info to the public. But I still would like to use the advantages of google + and use it as a marketing tool. So basically what I am ultimately wondering is, Is there anyway a website I use to earn money could come across, that basically My log-in email Is a google + account with a different name. Meaning i broke the TOS? Even though I truly didn't, becuase I gave all my true information to the website at signup. lol. I know this probably sounds very confusing. I think I just have to put my accurate name for Google + but just go into privacy settings and set it up to my liking. I just hope that I can still use Google + to it's full advantages after doing so. Does anyone else use Google + to market, get referrals, and traffic?