Say bye-bye to the service. People won't use it online if it's not relatively anonymous. And the only benefit to real names is to Google, not the user - and the users know this.
I once worked on a forum in a professional industry that crushed long established forums. One of the advantages we used was anonymous postings. Even when commenting on professional matters people didn't want their real information used. For example it allowed them to discuss pricing and product design in generic terms, without any of 'Oh, that's Bob from our competitor, handing out advice to Sally at another company'.