If everyone had two family names, one from mother and one from father, then the two names of child would be chosen one from the two names of the mother and one from the two names of the father. The choice could be random or by preference.
This would match the way how chromosomes are passed from the parents. Neglecting the crossover (whose effect is only that the sequence pairs between which a random choice is made are smaller than the chromosomes), for each pair of chromosomes one is taken from the mother and one from the father. The choice of which of the two chromosomes of the mother and of which of the two chromosomes of the mother are taken, is random.
I believe that this would be a better system for naming people. A random choice of which family name to take from each parent might be preferable, to avoid the reduction in number of the possible family names, if some would be preferred much more often than others.
This would match the way how chromosomes are passed from the parents. Neglecting the crossover (whose effect is only that the sequence pairs between which a random choice is made are smaller than the chromosomes), for each pair of chromosomes one is taken from the mother and one from the father. The choice of which of the two chromosomes of the mother and of which of the two chromosomes of the mother are taken, is random.
I believe that this would be a better system for naming people. A random choice of which family name to take from each parent might be preferable, to avoid the reduction in number of the possible family names, if some would be preferred much more often than others.