Get translated value of particular taxonomy term

First get current language

$language =  \Drupal::languageManager()->getCurrentLanguage(\Drupal\Core\Language\LanguageInterface::TYPE_CONTENT)->getId();

then load term with providing term id

$taxonomy_term = \Drupal\taxonomy\Entity\Term::load($term->tid);
$translated_term = \Drupal::service('entity.repository')->getTranslationFromContext($taxonomy_term, $language);

finally get the term name

$translated_term->getName()