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.

Geoffrey

Since WordPress 4.5, that feature is included in the Core. You don’t need this plugin anymore. Thank you all for support.
Adds the possibility for users to log in with its email address OR its username. 
Uses native WordPress functions. 
Lightweight plugin, no options, just activate it and it works!
Please, use the support forum to tell me bugs encountered, before rating the plugin. Be patient, it’s free, remember it 😉
Languages available:
<ul>
<li>Deutsch</li>
<li>English</li>
<li>French</li>
<li>Spanish</li>
<li>Russian</li>
</ul>
<h3>Other plugins</h3>
Find my plugins at <a href="https://profiles.wordpress.org/creativejuiz/" rel="nofollow ugc">https://profiles.wordpress.org/creativejuiz/</a>

Juiz User Log-in by email

Allows users log in with its email address OR its username

WooCommerce E-mail Login vs Juiz User Log-in by email