You will be sending emails to your users, from your server. This means you can edit template to your liking. Here we will explain how to override HTML template, and use your own logo. The unbranded version of the email will be send to your users. See below example.
MU Plugin
To change the template HTML, and therefore the possibility to change the logo you can use an MU plugin. You can change the logo by changing the URL https://downloads.really-simple-security.com/images/security.svg to your own logo. Save as custom-email-template-unbranded.html.
Proceed to drop below PHP file in your MU plugins folder, and make sure the folder structure looks like this:
wp-content/
|– mu-plugins/
| |– custom-email-template.php
| |– custom-login-logo.php (BONUS)
| |– custom-email-templates/
| |– custom-email-template-unbranded.html
Bonus: Change the logo on your WordPress login page
Add below MU plugin to also change the logo on your login page.