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.

imsoftware

This plugins replaces the regular authentication of WordPress and offers instead the authentication of users via IMAP accounts. Password reset and retrieving are suppressed in order to avoid confussion.
The IMAP authentication server as well as an automatic padding of the domain to a user name can be set on the plugins setting page under Settings > IMAP Authentication. Furthermore, users having a IMAP account on the defined server can automatically be register if set so.
Contributors: Aaron Parecki, Riccardo Magliocchetti, Lorenz Schmid, Marius Müller

WP IMAP Auth

Use IMAP accounts to login in to WordPress. Replaces the regular authentication.

WooCommerce E-mail Login vs WP IMAP Auth