In the Avengers, Loki is introducing himself as: Loki of Asgard. Doesn't he have a real surname? Like the surname of one of his fathers? :)
Nordic naming tends to consist of a first name and the name of the parent. Thor, would be Thor Odinson, the son of Odin.
Loki, however, is not Odin's son. He's adopted by him, but his father is the frost giant Laufey. As an adopted Asgardian, he can't very well call himself Loki Laufeyson, so Loki of Asgard it is. He is of Asgard, but the son of no Asgardian.
He is called 'Loki of Asgard' because the writers of the Marvel movies wanted to keep a bit of suspense as to where Loki came from. Remember the reveal with the Casket of Ancient Winters?
The naming convention of using one's first name and the name of one's home has been done since the fifth century so it is not an out of place custom, even among the Asgardians.
In the comics, however, he is indeed called Loki Laufeyson. It is well-known he was adopted by the All-Father Odin. If anyone is displeased by this, they tend to keep their opinions to themselves lest they suffer Odin's wrath.
- Loki Laufeyson is the son of Queen Farbauti and King Laufey, leader of the Giants of Jotunheim. King Laufey was the leader of the Giants of Jotunheim. He married Farbauti who bore him a son. However, he was born small and was kept in secret away from the other Giants for being an embarrassment to his parents. [Journey into Mystery #112]
if you ask me he should be named Loki Jotunheim. He was born there was he not? or at least he was half frost giant. And im pretty sure that Laufey was the MOTHER of Loki.
Loki could not take the name of his father since his father was a frost giant. It was bad enough he was an adopted son, do you think he would want to publicize that he was a son of the Asgardians' hated enemies? And as for the mother, Nordic naming traditions wouldnt allow him to take the mother's name. At least i think it wouldnt allow it.
Marvel made Laufrey the father, and also made "him" a frost giant,but regardless of that, saying Loki of Asgard would be the best solution for him so he wouldnt be outright saying he was a half-blood by calling himself Loki Laufeyson, or Loki Farbautison if you follow the mythology where Farbauti is the father. And as i said, Nordic naming would not let him take his mother's name in either case, at least that is what i believe. And for having a frost giant father, he couldnt take his name either.
Im only offering the name Loki Jotunheim because it is not too far off as he is half frost giant and also because it sounds cool. Loki of Asgard or even Loki Asgardson would be best but only half accurate as he is not entirely a "son" (native) of Asgard, only adopted. Loki could take Jotunheim as his surname but again he would not want to publicize his other bloodline is frost giant since he wants to rule Asgard. Of course, "Loki of Jotunheim" would also work as well as "of Asgard" or "Asgardson" but it just doesnt sound as good. Neither does Loki Jotunheimson.