View post with specific category id and name which I selected in the backend (drop-down option)

Try this code.

<?php $cat_id = get_theme_mod('cat_choose', $defaults); ?>
<p><?php echo get_cat_name( $cat_id ); ?></p>
<hr>
<?php
$args = array(
  'post_type' => 'post' ,
  'orderby' => 'date' ,
  'order' => 'DESC' ,
  'cat' => $cat_id,
  'posts_per_page' => -1,
); 
$cat_posts = new WP_query($args);
if ($cat_posts->have_posts()) : while ($cat_posts->have_posts()) : $cat_posts->the_post(); ?>
<div>
    <div>
        <h1><?php the_title(); ?></h1>
        <p><?php the_content(); ?></p>
        <p><?php the_time('F j, Y'); ?></p>
    </div>
    <div>
        <?php the_post_thumbnail(); ?>
    </div>
</div>
<?php endwhile; endif; ?>

Display Category Name using Category ID

<?php
$cat_id = get_theme_mod('cat_choose', $defaults);
echo get_cat_name( $cat_id );
?>