Hitachin
sweatdrop
you could've just googled it -
"
The short answer is that they don't have surnames, nor would those be a normal feature of the sort of pseudo-medieval oriental world that Avatar is set in.
Toph does have a sort-of surname ('Bei Fong') because she comes from a noble albeit but not royal family whereas Zuko, Ozai and Azula are royalty and are thus identified by their rank and station. Sokka and Kattara come from a peasant village and are unlikely to have or need a surname. Aang has no surname but would probably identify himself by his status as a Buddhist monk
In many Eastern cultures, surnames are derived from either tribal affiliation or position
Therefore; full names would be
Fire Lord Zuko
Fire Lord Ozai
Korra of the Southern Water Tribe
Avatar Aang Thich
Katara of the Southern Water Tribe
Sokka of the Southern Water Tribe" - Richard
THOSE ARENT NAMES! Those are titles. It kind of makes sense for the first series because it had a much more eastern theme, and I think the air nomads would have considered a surname an "attachment" so I get why aang wouldn't ever have a last name.
That would be like saying "Queen Elizabeth" is her name or "President Obama."
With the korra series I would expect everyone to have last names due to how western it is.