If you don't want your name passed to StackExchange, then you should not have clicked the button that allowed the credentials to be passed from your OpenID provider (whom I assume has your real name) to StackExchange.
See this article for a discussion. I quote
First, it's important to be cognizant of this data-sharing model -- that once you've shared the data, it's out the door and into the wild world, and there's not much you can do to get it locked back up. If that worries you, be really conservative with what data you share.
With that said: if you don't want your name associated, you can either
- Remove the real name from your OpenID provider. The next time you log-in the new credentials will have no real name field.
- Register for a separate anonymous OpenID account and use that for StackExchange. What you should do is to click on the "my logins" link in your profile, add the new OpenID account to it, and remove the old one.