You cannot connect the two different external Email Addresses to two different Organizations within Event Temple Chains as a User.

If under Organization 1. You have fake@email.com connected. You cannot connect a different external Email at Organization 2. Org 2 will automatically have fake@email.com connected. If you update your connected email address at anytime, it will automatically update in all Organizations you have access to.

If you are an Admin User you can choose who the email is sent from in the 'From Field' from all the emails that are connected to the Organization. This can be done by clicking on the "From Field" within the email