Check get_the_author()
(Note:This tag must be used within The Loop.)
you code may be like this
In functions.php:
add_action( 'save_post', 'add_authors_name');
function add_authors_name( $post_id ) {
global $post;
$post_author = $post->post_author; // returns the Author ID
// get the author's WP_User object so we can get the Author Name
$post_author_obj = get_userdata( $post_author );
$post_author_name = $post_author_obj->first_name . ' ' . $post_author_obj->last_name;
wp_set_post_terms( $post_id, $post_author_name, 'post_tag', true );
}