As my son is now venturing into the wide world of kindergarten, his name has become a topic of intense scrutiny as he joins a larger society so I thought I would add a few other details to the Spanish names node. Since I have stubbornly held on to my traditional hispanic name, my wife and I have saddled him with two given names and a hyphenated family name. The resulting name is more than a bit weird since my wife has a German family name.
Why use two family names at all? - Though I am nobody, in Spain and other Hispanic countries, family is a strong bond and traditionally an indicator of your place in society. For example, before the Sandinistas came to power in Nicaragua, the Somoza family owned 23% of the arable land so you can imagine that your family name was important, even if it was just from your Mother's side. In times of decadence, people have been known to continue to tack on family names using the same formula until they hit an important name.
Familiy names, marriage and women - Because the names from both branches of the family are important, women do not usually assume their husbands family name. Though it has fallen into disuse except in the most refined "society" context, women would drop their mother's maiden name and attach the husband's family name to their own using "de" (of) to connect them. Hence if Maria Elena Jimenez Gonzalez were to marry Juan Francisco Rodriguez Sanabria she would change her name to Maria Elena Jimenez de Rodriguez. If Juan were to die before her, she would become Maria Elena Jimenez vda de Rodriguez where vda is an abbreviation for "viuda" (widow). All these machinations happen only in a social context mind you, all official documents will carry the maiden names of the woman only.
Religion and given names - The use of two given names is common in Hispanic countries as well, and the roots can be found in religion. In order to get baptised in the Catholic Church, you need to have been given the name of a saint. If your parents insisted on giving you a non-sainted name, like Marlene, then you needed a baptismal name, like Mary. French, Spanish and Polish men are also sometimes given a female middle name, like Marie or Maria. Hispanic women, similarly, sometimes have the middle name Juan. This is particularly common in Roman Catholic families, as a way to hedge your bets and get "divine protection" from both the male trinity and the Virgin Mary.
Please don't take all this as gospel though. I was born and grew up in the Caribbean, so if you are from another part of the Spanish speaking world, your mileage may vary.