Index user_login instead of display name

<?php

// Add to your (child) theme's functions.php
add_filter( 'facetwp_index_row', function( $params, $class ) {
    if ( 'post_author' == $params['facet_source'] ) {
        $user = get_user_by( 'id', $value );
        if ( false !== $user ) {
            $params['facet_display_value'] = $user->user_login;
        }
    }
    return $params;
}, 10, 2 );