In Iceland, past and present, first names are the important ones (catalogues such as the phone book are all listed by first name), as everybody gets a patronymic as a last name, and women don't change their last name upon marriage. So, if you have a family of two parents, and a son and daughter, they will all have different names. Hence, the importance of first names.
OK, so I know it's kind of random, but hey it's interesting.
What about Chinese names? You have the family name, then the generation name, and then your own name. Others have mentioned a religious link, but since Abrahamic religion in China originates from outside influence, their naming practices probably stem from other (still, perhaps religious?) concepts.
Hild