Is it possible to unset private_tempstore values?
delete() is the method to delete a value in the store.
$session = \Drupal::service('user.private_tempstore')-&gt;get('achva_sso');
$session-&gt;delete('name');

'name' is the value passed as first argument in any call to set().
You don't use PrivateTempStore::delete() since it's not a static method and it would throw errors or warnings, if called as static method.
As side note, user.private_tempstore is a deprecated service. Instead, the tempstore.private service should be used. (See User module's user.private_tempstore and user.shared_tempstore services moved to core for more details.) In the latest Drupal 8.5.x version, the service is marked as deprecated directly in the user.services.yml file.
class: Drupal\user\PrivateTempStoreFactory
arguments:
  - '@keyvalue.expirable'
  - '@lock'
  - '@current_user'
  - '@request_stack'
  - '%tempstore.expire%'
deprecated: 'The &quot;%service_id%&quot; service is deprecated. You should use the ''tempstore.private'' service instead. See https://www.drupal.org/node/2935639.'
tags:
  - { name: backend_overridable }

It should also be better to use dependency injection: A class extending BlockBase, or ControllerBase, can implement the create() method to load new dependencies.