Alessandro Raffa

In some cases you want your wordpress users to login with their email address instead of the username. To do this, you can use a good plugin like ‘WP Email Login’ or you can activate a ‘Register Plus Redux’ plugin’s option, but when the users will ask for lost password, the old / original username will be emailed to them, and this can cause confusion. To avoid this situation, just install and activate Login Email Sync, and it will sync the username ( user_login database field ) with the email ( user_email database field ) every time a user updates her/his profile.
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Login Email Sync

In some cases you want your wordpress users to login with their email address instead of the username. To do this, you can use a good plugin like &#03 …

cubecolour

WordPress 4.5 added the ability to login using the registered user’s email address in place of the username. When this plugin is active, the ability to login using the email address in place of the username is removed, and the label of the input field is changed to reflect this.

No Login by Email Address

Removes the ability to login using the email address instead of the username.

Login Email Sync vs No Login by Email Address