Hiding Usernmaes/Emails from Google

I’ve got a website with sensitive (medical) subject matter, which people are not necessarily keen on having google associate their names. However, even though warned, some users sign up using their real names as their usernames.

Is there a plugin or mod which will block google from associating usernames and emails with the website, thus keeping google from putting our site in google search results when people google themselves?

Really appreciate the help. This is causing some bad PR.

Thanks!