Google's OpenID service links permissions for Google user IDs with specific domains. If a customer registers a store account using their Google user ID when accessing your site via your primary domain name, and you later change your store's primary domain name, Google will no longer recognize the customer's Google user ID as being registered with your store.

Should you change your store's domain name after a customer registers using their Google user ID, the customer will not be able to access their previously registered store account, and must register a new store account with either the same Google user ID, or another existing Yahoo, Google, AOL, or Facebook user ID.