Create dynamic logo carousel without using any plugin

You can create a custom post type for the logos as shown below,

function create_post_type() {

 register_post_type( 'logo',
   array(
     'labels' => array(
        'name' => __( 'Logos' ),
        'singular_name' => __( 'Logo' ),
        'add_new' => __( 'Add New' ),
        'add_new_item' => __( 'Add New Logo' ),
        'featured_image' => __( 'Add Image' ),
        'edit_item' => __( 'Edit Logo' )
     ),
   'public' => true,
   'menu_icon' => 'dashicons-images-alt2',
   'has_archive' => true,
   'rewrite' => array('slug' => 'logo'),
   'supports' => array('title','thumbnail'),
  )
 );
}
add_action( 'init', 'create_post_type' );

Add the above code in your theme’s functions.php file.

Then you replace your static logos with post loop.