anyway, how do they choose who takes the others last name? 
um, they both took each other's last name
in the US there aren't any strict rules on such things, but for both same and opposite sex marriages generally you keep your original name first. but then you and your partner have different last names, which may be confusing if you have children. often in opposite sex marriages, the man's last name will come first.
My former roommate and his partner have adopted two children (open adoptions, was there for both births, got to catch the first). His partner's name is Bell, his name is Knapp. Children's names are Belknap.
