At the moment there is no opportunity to change the email address at the account. You can create a new account with your new email address and synchronize all saved business cards with it. Please, do the following:
1. Synchronize business cards with ABBYY Account using your current account (email address): How do I synchronize my business cards?
2. In ABBYY BCR tap Settings > ABBYY Account > Sign Out;
3. Tap Register button and use a new email address;
4. Check that synchronization is turned on.