Du kan bruge distinct søgeord inde i array_agg :
SELECT ARRAY_TO_STRING(ARRAY_AGG(DISTINCT CONCAT(u.firstname, ' ', u.lastname)), ', ')
FROM log_has_item logitem
INNER JOIN log log ON log.id = logitem.log_id
INNER JOIN worker u ON log.worker_id = u.id
WHERE logitem.company_id = 1