Send Custom welcome email to specific user group

You have your functions mixed up – the new_mail_from is for the address, not the name, and the new_mail_from_name is for the name, not the address.

Also, WordPress changed the tests for users/groups from the old Roles to the new Capabilities so assuming your “buyer” user group has some specific Capability you can target then you could do something like this:

    // Change default WordPress email address for Buyers
    if(current_user_can( 'something_only_buyers_can_do' ) {
       function new_mail_from($old) {
       return '[email protected]';
     }
       function new_mail_from_name($old) {
       return 'Your Site';
     }
    add_filter('wp_mail_from', 'new_mail_from');
    add_filter('wp_mail_from_name', 'new_mail_from_name');

    }

You could still try using the old Roles but no telling how long that will work, using Capabilities is more future-proof.