I don't know the exact way the system works and what information exactly you share, @chaud is the man in charge that can tell you relevant things about that, but I can take away some of the other doubts that people have expressed:
1) No we won't know your real name
2) No not every moderator has access to the information you share. Me nor any of the other globals, nor any of the normal (green) mods have access to such information. Admin only (and I'm pretty sure even most of the admins won't have direct access to the information you share).
Far as I know this system is just to let people log on in a more secure and easy way, and to gather some more precise info that anyone could get without this log in anyway through Blizzard's API. That API is what chaud already uses when he's done news posts about achievement completion % etc, like the one about Proving grounds a few days ago.
There's really nothing sinister about it.