add_new_fields_during_registration_woocommerce.php

<?php
/**
 * Add new register fields for WooCommerce registration.
 */
function wooc_extra_register_fields() {
    ?>

    <p class="form-row form-row-first">
    <label for="reg_first_name"><?php _e( 'First name', 'woocommerce' ); ?> <span class="required">*</span></label>
    <input type="text" class="input-text" name="first_name" id="reg_first_name" value="<?php if ( ! empty( $_POST['first_name'] ) ) esc_attr_e( $_POST['first_name'] ); ?>" />
    </p>

    <p class="form-row form-row-last">
    <label for="reg_last_name"><?php _e( 'Last name', 'woocommerce' ); ?> <span class="required">*</span></label>
    <input type="text" class="input-text" name="last_name" id="reg_last_name" value="<?php if ( ! empty( $_POST['last_name'] ) ) esc_attr_e( $_POST['last_name'] ); ?>" />
    </p>

    <div class="clear"></div>

    <?php
}
add_action( 'woocommerce_register_form_start', 'wooc_extra_register_fields' );

/**
 * Validate the extra register fields.
 *
 * @param WP_Error $validation_errors Errors.
 * @param string   $username          Current username.
 * @param string   $email             Current email.
 *
 * @return WP_Error
 */
function wooc_validate_extra_register_fields( $errors, $username, $email ) {
    if ( isset( $_POST['first_name'] ) && empty( $_POST['first_name'] ) ) {
        $errors->add( 'first_name_error', __( '<strong>Error</strong>: First name is required!', 'woocommerce' ) );
    }
    if ( isset( $_POST['last_name'] ) && empty( $_POST['last_name'] ) ) {
        $errors->add( 'last_name_error', __( '<strong>Error</strong>: Last name is required!.', 'woocommerce' ) );
    }
    return $errors;
}
add_filter( 'woocommerce_registration_errors', 'wooc_validate_extra_register_fields', 10, 3 );

/**
 * Save the extra register fields.
 *
 * @param int $customer_id Current customer ID.
 */
function wooc_save_extra_register_fields( $customer_id ) {
    if ( isset( $_POST['first_name'] ) ) {
        // WordPress default first name field.
        update_user_meta( $customer_id, 'first_name', sanitize_text_field( $_POST['first_name'] ) );
    }
    if ( isset( $_POST['last_name'] ) ) {
        // WordPress default last name field.
        update_user_meta( $customer_id, 'last_name', sanitize_text_field( $_POST['last_name'] ) );
    }
}
add_action( 'woocommerce_created_customer', 'wooc_save_extra_register_fields' );
?>