Currently for the Assign a Task action, if you use do not use LazyApproval option, the email comes from the name of the site. If you use Lazy Approval, it comes from Nintex email (firstname.lastname@example.org).
Is it possible to use the Nintex external email as the sender for a Task **NOT** using LazyApproval?
Tasks are meant to be assigned to members of a SharePoint tenant and that is why there is no external email setting as there is in the send notification action. For Lazy approval to work it needs external infrustructure. The side affect is that you can sent Tasks to external users.