How can I programmatically change the active theme?
In Drupal 8, you use theme negotiators, which essentially are services using a specific tag. See the theme negotiators implemented by Drupal, to understand exactly how they work; the example given in the change record is not updated.
user.services.yml
  theme.negotiator.admin_theme:
    class: Drupal\user\Theme\AdminNegotiator
    arguments: ['@current_user', '@config.factory', '@entity_type.manager', '@router.admin_context']
    tags:
      - { name: theme_negotiator, priority: -40 }

AdminNegotiator.php
&lt;?php

namespace Drupal\user\Theme;

use Drupal\Core\Config\ConfigFactoryInterface;
use Drupal\Core\DependencyInjection\DeprecatedServicePropertyTrait;
use Drupal\Core\Entity\EntityTypeManagerInterface;
use Drupal\Core\Routing\AdminContext;
use Drupal\Core\Routing\RouteMatchInterface;
use Drupal\Core\Session\AccountInterface;
use Drupal\Core\Theme\ThemeNegotiatorInterface;

/**
 * Sets the active theme on admin pages.
 */
class AdminNegotiator implements ThemeNegotiatorInterface {
  use DeprecatedServicePropertyTrait;

  /**
   * {@inheritdoc}
   */
  protected $deprecatedProperties = ['entityManager' =&gt; 'entity.manager'];

  /**
   * The current user.
   *
   * @var \Drupal\Core\Session\AccountInterface
   */
  protected $user;

  /**
   * The config factory.
   *
   * @var \Drupal\Core\Config\ConfigFactoryInterface
   */
  protected $configFactory;

  /**
   * The entity type manager.
   *
   * @var \Drupal\Core\Entity\EntityTypeManagerInterface
   */
  protected $entityTypeManager;

  /**
   * The route admin context to determine whether a route is an admin one.
   *
   * @var \Drupal\Core\Routing\AdminContext
   */
  protected $adminContext;

  /**
   * Creates a new AdminNegotiator instance.
   *
   * @param \Drupal\Core\Session\AccountInterface $user
   *   The current user.
   * @param \Drupal\Core\Config\ConfigFactoryInterface $config_factory
   *   The config factory.
   * @param \Drupal\Core\Entity\EntityTypeManagerInterface $entity_type_manager
   *   The entity type manager.
   * @param \Drupal\Core\Routing\AdminContext $admin_context
   *   The route admin context to determine whether the route is an admin one.
   */
  public function __construct(AccountInterface $user, ConfigFactoryInterface $config_factory, EntityTypeManagerInterface $entity_type_manager, AdminContext $admin_context) {
    $this-&gt;user = $user;
    $this-&gt;configFactory = $config_factory;
    $this-&gt;entityTypeManager = $entity_type_manager;
    $this-&gt;adminContext = $admin_context;
  }

  /**
   * {@inheritdoc}
   */
  public function applies(RouteMatchInterface $route_match) {
    return ($this-&gt;entityTypeManager-&gt;hasHandler('user_role', 'storage') &amp;&amp; $this-&gt;user-&gt;hasPermission('view the administration theme') &amp;&amp; $this-&gt;adminContext-&gt;isAdminRoute($route_match-&gt;getRouteObject()));
  }

  /**
   * {@inheritdoc}
   */
  public function determineActiveTheme(RouteMatchInterface $route_match) {
    return $this-&gt;configFactory-&gt;get('system.theme')-&gt;get('admin');
  }

}

The code is pretty easy to understand: The applies() method returns TRUE when the current route is the one for which your module wants to change the theme; the determineActiveTheme() method returns the theme machine name of the theme to apply.
See also ThemeNegotiator::determineActiveTheme() should not require a RouteMatch to be passed in for a possible change on the arguments received from the methods used by theme negotiators; if that patch is applied, you will need to change your theme negotiator code too.
That issue's status has been Needs work since May 10, 2018; it has been also moved to Drupal 9.2.x on December 28, 2018. Drupal 8.9.x could not get that change back-ported and it's probably safe to say that a Drupal 8.x module needs to use the RouteMatchInterface $route_match parameter for applies().