Well aren't You overdoing it a little bit? Scared of giving Your name? Don't be ridiculous now. I mean I use internet for about 17-18 years now.
The issue is people are both paranoid and hypocrites about some things. One one hand They will have fully fleshed out FB profile, with their full name, address, schools They did attend, friends with similar set of information, etc. while on the other They get all bothered because some corporation will use the data about Their gaming preference. Really now?
Just like You don't go around waving Your ID around in public, You don't do it on the internet, sure, that's obvious, but that doesn't mean You have to cover Your face whenever You go near the window, does it?
Personally I'm not really troubled by the fact that my name exists in some table somewhere as someone who bought certain games or used certain web services. It really doesn't affect my life at all.
Common sense is really all You need. Don't have passwords that tie to Your dates/SSN/names/etc., have separate e-mail (or few) for various sign-ups so You don't clog Your main account, don't store Your credit card info in plaintext on Your HDD ... just like outside of internet You shouldn't carry Your CC pin on a note along with Your card, etc.