In the common case where names are
so assigned, the part of a person's
name which identifies the family
of which the person is a member.
In ``Western'' cultures, this is
generally the last name.
Compare with given name.

English family names started around the Middle Ages as a way of distinguishing between different classes. As time passed familly names were also based on occupation, such as Forester or Baker, or where the familly lived, such as York. Familly Names also came from they way the familly looked or were patronymic, which is related to ancestry(the male side at least) such as David's son; Davidson.

Another source of family names was simple human habit. Imagine someone who's come to a country where use of family names is rare. He'll meet someone, and ask for their name. They might reply with any of the following:

I am Rahim iben Saiid iben Naruk iben Ahmed iben ... (Ad Nauseam)

My name is Ander Mac Reng

From the family Pai-Je, I am Chi-Lo.

I am Bull-Neck from the tribe of the Bear All of which might be shortend by our hypothetical traveler to something like:

Rahim iben-Saiid

Ander MacReng

Pai-Je Chi-Lo

Bull-Neck Bear

Now, assuming the person he addressed liked the name he gave them (instead of lopping his head off for the insult) - this might become what they called themselves. I doubt this happened, but it's all too possible, seen as how lazy people were in obeying the customs of others.