Sword Art Online: Alicization has been a big hit with fans so far as the series put Kirito smack dab into a brand new virtual world with brand new rules, but just because he's in new surroundings doesn't mean Kirito has forgotten his virtual reality past.
After finally levelling up to the point where he can use a sword, Kirito is asked what sword style he uses and the name of it should sound familiar with Kirito's season one adventures in Aincrad.
In the latest episode, Kirito and Eugeo find themselves battling against a group of goblins in order to save the kidnapped Selka. Kirito successfully defeats the goblin boss after several traded blows, and Eugeo is saved from the brink of death by Selka. After this, Eugeo decides to become a swordsman and asks Kirito to teach him.
Kirito agrees, but Eugeo asks what Kirito's sword style is called and, after thinking for a moment, Kirito names his style "Aincrad Style." Aincrad was the name of the original virtual world Kirito and the others found themselves trapped in during the first season of the series. There's been evidence throughout the third season already that the character's time in Aincrad still has an effect on them (which is something the second season hinted at, but didn't touch on too much), but this is a great way for Kirito to flip that trauma.
This new world, the Underworld, has had some similarities with Aincrad's virtual world as Kirito's sword skills have been translated well enough, but this is Kirito's way of directly connecting the two. His sword style had yet to get an official name in the series, but this goes to show how Kirito's now using his stolen time to better his experiences going forward. Especially now that he has a student in Eugeo who will carry on this style as well.
Sword Art Online: Alicization can currently be found streaming on Crunchyroll, Funimation, and Hulu. The series is described as such:
"Where... am I...?" Before he knows it, Kirito has made a full-dive into an epic, fantasy-like virtual world. With only a murky recollection of what happened right before he logged in, he starts to wander around, searching for clues. He comes upon an enormous, pitch dark tree (the Gigas Cedar), where he encounters a boy. "My name is Eugeo. Nice to meet you, Kirito." Although he is supposedly a resident of the virtual world - an NPC - the boy shows the same array of emotions as any human being.
As Kirito bonds with Eugeo, he continues to search for a way to log out of this world. Meanwhile, he remembers a certain memory deep down within him. He remembers racing through the mountains with Eugeo as a child... A memory that he should not have in the first place... And in this memory, he sees someone other than Eugeo, a young blond girl. Her name is Alice. And it is a name that must never be forgotten..."