While there are alternative explanations for how the naughty/nice list is generated, hashing is important: Santa could be using a Bloom filter, in which false positive matches are possible, but false negatives are not (i.e. a query returns either “possibly in set” or “definitely not in set”, thus it has a 100% recall rate).
And while we’re on this subject, remember Santa’s delivery route represents a nested Travelling Salesman Problem, compounded by the naughty/nice list changing every year…
(Merry Christmas…and watch out!)