X-23:
She is the young mutant who possess Wolverine’s DNA. In the movie, she is among several test subjects but in comics, she is a full-blown Weapon-X successor who was freed to find a path of her own. Also, she put an X sign beside Logan’s grave.
Old Man Logan:
The character of Wolverine in the movie is inspired by “Old Man Logan” story based on a dystopian future where villains finally prevailed over Wolverine when supervillain Mysterio laid a trap.
Berserker rage:
As expected, we saw berserker rage from X-Men comics i.e a mental state when Wolverine turns absolutely crazy, goes on a rampage, without thinking about the moral consequences of the act.