WooCommerce change new customer's auto generated username format.

functions.php

<?php
/**
 * Custom new username for new customer.
 *
 * @param string $username Username.
 * @param string $email Email.
 * @param array  $new_user_args New user args.
 * @param string $suffix Suffix.
 *
 * @return string
 */
function custom_new_customer_username( $username, $email, $new_user_args, $suffix ) {
	$billing_first_name = isset( $new_user_args['first_name'] ) ? $new_user_args['first_name'] : '';
	$billing_last_name  = isset( $new_user_args['last_name'] ) ? $new_user_args['last_name'] : '';

	$new_username = sanitize_user( strtolower( $billing_first_name . '.' . $billing_last_name ) );

	if ( username_exists( $new_username ) ) {
		return append_random_number( $new_username );
	}

	return $new_username;
}

add_filter( 'woocommerce_new_customer_username', 'custom_new_customer_username', 10, 4 );

/**
 * Append random number to username if it already exists.
 *
 * @param string $username Username.
 *
 * @return string
 */
function append_random_number( $username ) {
	$random_number = wp_rand( 1, 999 );
	$new_username  = $username . $random_number;

	if ( username_exists( $new_username ) ) {
		return append_random_number( $username );
	}

	return $new_username;
}