Изменение e-mail в настройках администрирования wordpress, добавляется в файл functions.php

add_option_new_admin_email

remove_action( 'add_option_new_admin_email', 'update_option_new_admin_email' );
remove_action( 'update_option_new_admin_email', 'update_option_new_admin_email' );

/**
 * Disable the confirmation notices when an administrator
 * changes their email address.
 *
 * @see http://codex.wordpress.com/Function_Reference/update_option_new_admin_email
 */
function wpdocs_update_option_new_admin_email( $old_value, $value ) {

    update_option( 'admin_email', $value );
}
add_action( 'add_option_new_admin_email', 'wpdocs_update_option_new_admin_email', 10, 2 );
add_action( 'update_option_new_admin_email', 'wpdocs_update_option_new_admin_email', 10, 2 );