Garner
Lukes last name is Garner
Luke's last name is Triton.
Luke is a diminutive of the name Lucas, from the Latin Lucius meaning "shining one".
Luke's last name is Castellan in the Battle of the Labyrinth, and in all the other books in the Percy Jackson and the Olympians series.
Jackson
His new name is Lee Grant
Lucas is the son of Luke
Castellan.
I believe it was never revealed.
The last name of Luke or Lucas originates from several different European countries: it can't be situated without knowing a bit more about your family history. In addition, "Luke" is a spelling of a common Cantonese name and/or Vietnamese name--so it could come from there, too.
His kast name is Skywaljer, Luke Skywalker
Luke Steinberg. No, just kidding, there is nothing in the bible that indicates a last name, and nothing in history that I am aware of that does either.