show limited tags in an article

Your code with changes:

<?php 
    $post_id = get_the_ID();
    $queried_post = get_post($post_id);
    $user_info = get_userdata($post->post_author);  // <-- or: $user_info = get_the_author_meta('ID')
    $first = $user_info->first_name;   // what if it is empty or contains forbidden characters?
    $last = $user_info->last_name;    // as obove
    wp_set_post_tags( $post_id, $first, true );   // <-- tag slug, used in the code below

    // --- display tag ---
    if ( has_tag("$first") )
    {
        $author_tag = get_term_by( 'slug', "$first", 'post_tag' ); 
        if ( $author_tag instanceof WP_term )
        {
            $a_name = $author_tag->name;
            $a_link = get_term_link( $author_tag->term_id );
            // display tag
            echo '<a href="' . esc_url( $a_link ) . '" rel="tag">' . $a_name . '</a> ';
        }
    }

?>

Personally, I would move the code adding the tag to action hook save_post_{post_type} and execute when $update parameter is FALSE (a new post was created).

add_action( 'save_post_post', 'se337414_add_author_tag', 20, 3 );
function se337414_add_author_tag( $post_id, $post, $update )
{
    // create tag only when post is created
    if ( $update == true )
        return;

    $user_info = get_userdata( $post->post_author ); 
    $tag_parts = [];
    if ( !empty($user_info->first_name) )
        $tag_parts[] = $user_info->first_name;
    if ( !empty($user_info->last_name) )
        $tag_parts[] = $user_info->last_name;

    $tag_slug = implode( '-', $tag_parts );
    if ( empty($tag_slug) )
        return;

    wp_set_post_tags( $post_id, $tag_slug, true );
}