Avatar: The Last Airbender

My anecdotal understanding is that Chinese surnames are ancient, being commonly used by the masses in times before the Caesars ruled Rome. In the earliest days there were only surnames for noble families but they became pretty commonplace very quickly. My own surname denotes an ethnic group, but others may be professions, titles, or regional identifiers.

IIRC, Japanese surnames are more recent, with only clan names of prestigious families in use prior to the 1800's (e.g. Taira no Kiyomori, Kiyomori of the Taira). When Japan westernized and mandated that people adopt surnames, the majority ended up being some kind of geographical/positional/professional descriptor. A common Japanese name, Tanaka 田中, is made of the Chinese characters for "field" and "middle", so it roughly means "in the field" and indicates someone who was probably descended from a farmer. Another common name, Yamashita 山下, is made of the Chinese characters for "mountain" and "below" and indicates someone whose ancestors probably lived at the foot of a mountain.

I know nothing about Korean names since they aren't written in Hanzi, but I know they used to be, so it wouldn't surprise me if it was a similar situation. I likewise can't speak to other countries in central Asia or SEA.