According to "TheBlack Box", which is the avatar name of a Second Life user, Google allowed him to keep his Google+ social network account named after that pseudonym. After changing the G+ account name from his real life name to his SL avatar name, his account was flagged, and he sent Google this SL group website link, to prove he was known as TheBlack Box by over 2500 SL users. After some more back and forth, as he reports on his active Google+ account, Google eventually sent him this e-mail:
"Thanks for sending us your appeal. You're right: your name does comply with the Google+ Names Policy. Your name has been updated on your Google+ profile. If you submitted the appeal during sign up, your profile has now been restored. Log in to Google+. Sorry for the inconvenience, The Google+ team."
And so now TheBlack Box in SL is officially TheBlack Box on Google+. This is evidently evidence that Google will indeed allow at least some SL avatars to go by their pseudonym on Google+, when provided sufficient evidence that the avatar name is well-established. When I spoke with her on Tuesday, a Google spokesperson was cagey on what kind of evidence they would accept for pseudonymous G+ accounts. And different Google policy review staffers may make different decisions. But at least in The Black Box's case, a pseudonym-only avatar name was apparently allowed.
Hat tip: Botgirl Questi.