  We study the frequency distribution of family names. From a common data base,
we count the number of people who share the same family name. This is the size
of the family. We find that (i) the total number of different family names in a
society scales as a power-law of the population, (ii) the total number of
family names of the same size decreases as the size increases with a power-law
and (iii) the relation between size and rank of a family name also shows a
power-law. These scaling properties are found to be consistent for five
different regional communities in Japan.
