I've been thinking about names -- surnames and family names -- and mostly in the context of my story; as in, what type of last names should characters have, if they have any. It started a couple weeks ago with a discussion of medieval names with
londubh, continued through a google search, a conversation the other day with
traumerin about international last names, and another google search. (And might I add that google is not your friend when searching for something like "history of surnames." Go ahead, type it in, see what you get. Creativity with search topics doesn't really help either.)
Still, I seem to have gathered some general ideas about the purpose of last names. Nonhereditary last names seem to fill a slightly different function than hereditary ones -- or rather, they fill the same purpose, but for a different reason. Names as a whole are descriptive and/or markers: they tell people who you are, and how you are different from someone else. Nonhereditary names, then, would more likely fill the descriptive function than just being a marker (for example, "dark haired girl" rather than "sophie." One has a meaning we recognize while the other, on the whole, is merely a collection of syllables). Even "son/daughter of" surnames would be descriptive if you knew the father or mother.
Hereditary surnames, then, would serve a similar purpose of describing a person, but add familial information. Some reasons I thought of might be:
1) Information on a group of people -- your family -- is made necessary by paper-makers, aka government. This probably aids in keeping track of people. If your last name is something you're born with, and not something you gain, it adds a descriptive. Though this is true of "son/daughter of" surnames as well (except for the group part).
And considering that in Iceland people still go by "son/daughter of" surnames, and the phonebook is listed by first name (thank you
traumerin for that trivia) then I'm not sure why an hereditary family name would be necessary for a bureaucracy. Although the one helpful website I found mentioned "Government became more and more a matter of written record. As the activities of government, particularly in the levying of taxation and the exaction of military service, touched an ever widening range of the population, perhaps it became necessary to identify individuals accurately."
2) You want to be known by who you are related to and therefore who you know. If you're related to royalty, say, and an hereditary last name shows this, that would be a benefit if you're trying to gain prestige.
Or to combine 1 and 2, if information on a group of people is made necessary by the group itself, that can create an hereditary surname. For example, hereditary clan names for peoples that consider history and geneology important.
3) And last thought, once again from the one helpful article: if hereditary surnames first became fixed through hereditary lands, and the lower class tried to imitate the upper class to be thought better, they would create hereditary surnames as well.