Access first name and last name from user_register

The Codex is always a good place to look for things. Check out this https://codex.wordpress.org/wp_get_current_user

Where you will find this sample code:

<?php
    $current_user = wp_get_current_user();
    /**
     * @example Safe usage:
     * $current_user = wp_get_current_user();
     * if ( ! $current_user->exists() ) {
     *     return;
     * }
     */
    echo 'Username: ' . $current_user->user_login . '<br />';
    echo 'User email: ' . $current_user->user_email . '<br />';
    echo 'User first name: ' . $current_user->user_firstname . '<br />';
    echo 'User last name: ' . $current_user->user_lastname . '<br />';
    echo 'User display name: ' . $current_user->display_name . '<br />';
    echo 'User ID: ' . $current_user->ID . '<br />';

Which uses the WP_User object: see https://codex.wordpress.org/Class_Reference/WP_User .