How to show only category name?

See if the template tag, wp_list_categories will produce satisfactory output for you.

If that won’t work for you then you’ll need a special query so take a look at Function_Reference/wpdb_Class.

Open category-template.php [its a file that comes with WP and is located in the wp-includes directory] in your favorite editor. Remove references to li & a and then upload file to wp-includes directory on your web server.

This echos all categories considered post categories:

<?php
$mycategories = $wpdb->get_col("SELECT cat_name FROM $wpdb->categories WHERE category_count > 0 ORDER BY cat_name");
   if ( ! empty($mycategories) ) {
      foreach ( $mycategories as $mycats ) {
        echo $mycats;
      }
   }
?>

Thanks. ??