By default, you and your customers will have to login using your username. This is not practicall since WooCommerce will auto-generate usernames for your customers and they will often forget what their username is. This plugin will resolve that by enabling your users to login using their e-mail address.
<ul>
<li>Works with WooCommerce</li>
<li>Perfect with Klarna Checkout</li>
</ul>

WooCommerce E-mail Login

Enables you and your customers to login with your e-mail address as well as your username.

DigiP

This is a Security focused plug-in, which will send an email to the Administrator of the WordPress site each time login page is reached.
If someone attempts to login, it will also send the user name they tried logging in with, as well as their IP address, User-Agent, Timestamp, and the Referral URL.
If you see multiple attempts to login at times you are not logged on to the site, this means someone is attempting to brute force their way into your site, and you should ban the offending IP address from your site. Especially if they are trying multiple names, or sending them rapidly, one after another.
<h3>Thank you for using my plug-in!</h3>
We offer a variety of other products and security solutions for WordPress and web site security. We’re in the process of releasing our WordPress Attack Scanner, as well as a Firewall based version of the same scanner for paid subscribers.
For more info on these tools and products, please visit and bookmark Attack-Scanner.com, and if you like this Login Alerts Plug-in, please donate to this project.
I look forward to feedback from my users, as well as feature requests. All and any feedback welcome!

WP Login Alerts by DigiP

E-mails the site owner if anyone reaches or attempts to login to the site. Also shows the user names they attempt to login with.

WooCommerce E-mail Login vs WP Login Alerts by DigiP