If you are using LightOpenID, $openid->identity
will be unique identity to store in database.
And some OpenID Provider(OP) like google support AX extensions, that I use it to build up user profile by getting their first name (to address them in the future) and email (for contact) and store it in database.
And LightOpenId already support AX extensions. Example:
//required attribute(s)
$openid->required = array('namePerson/first', 'contact/email');
//optional attribute(s)
$openid->optional = array('namePerson/last');
If OP does not support AX, you can let user to choose their desire name, like SO currently does.
Some good resource I refer to when integrating LightOpenId: