automatically create an private OG when user register

Hi,

First of all, I'm not english so I apologize for my bad english...

My goal is to create a group (named different from username) when user register, and this one will be private.
Example : Mike create an account and in the same time a group named "family" is created and it's private.

I find a way to create a group when user register (Bundles : user > Fields : group - group), but the group name = username.
And I can't my this group private, I got "Field Group visibility can only be attached to Node entity bundles."

How can I override this one ? And a groupname different from the username is it possible ?

Thank you for your answers !