Paul said "you both give your daughters the part of your name you got from your mother and sons the part you got from your father - it in effect creates a matrilineal line for women and a patrilineal line for men."

I like the Icelandic system. Daughters get as their surname their mother's first name with -dottir on the end. Sons get as their surname the father's first name with -son on the end. So a family with two parents and a child of each sex has four surnames. This shows links of descent, but not biased to one sex, and doesn't make surnames precious. Perhaps consequently, I'm told, the Icelandic phone book is sorted by first name.