From survey data on surnames in an immigrant community of Indians in Houston, Texas, it is shown that the family size distribution and the distribution of the number of male children per family are independent of the surnames of the parents. This provides a direct test of selective neutrality of surname distributions. A genetic theory of sampling distribution of neutral alleles is employed to estimate the parameter of the surname distribution, and analytical results for the expectation and variance of the frequencies of surnames with a different number of copies in a sample are provided. It is also shown that the surname distribution may indicate presence of mixture in a sample, which can be examined by such theoretical approaches. The transition of surname distributions in two successive generations is shown to follow the pattern predicted by random extinction of surnames.