Is Carnage a Child of Venom?
The most obvious way Sony could rewrite Carnage's backstory for Venom 2 is to mesh the movie setup with the comics. Cletus Kasady breaks out of San Quentin and, true to his word, targets Eddie Brock. Based on that diary backstory, Kasady's goal won't just be to kill Brock; he'll want Eddie to lose everything first. That opens up the notion of Kasady first targeted the people Eddie cares about, ranging from friends to colleagues to his ex. Brock may be able to protect himself from Kasady, but will even Venom be able to keep everyone around him safe from the maniac's ire?
Meanwhile, another sub-plot could see the Venom symbiote reproduce. Perhaps Venom hopes its spawn will bond with Anne Weying, as part of a wrong-headed desire to bring her back into Eddie's life. But the young symbiote wouldn't cross paths with Anne; instead, it would be found by Kasady. Young and vulnerable, the symbiote would be overwhelmed by Kasady's own homicidal nature, and thus Carnage would be born.
This is a simple concept, and it could make for quite a chilling film as Kasady and Brock play a dangerous game of cat-and-mouse even before Cletus truly becomes Carnage. Unfortunately, it doesn't really explain why the Carnage symbiote's powerset is so different to Venom's. That raises the second possibility.
Is Carnage Another Team Leader?
But will Venom 2 go bolder? It's easy to forget that the symbiotes are still coming en masse. Venom revealed that the symbiote race had discovered life on Earth, with the comet stumbled upon by the Life Foundation was their idea of a spaceship. We don't know how long the symbiotes had been traveling before the Life Foundation picked up some samples - inadvertently granting the symbiotes an advance scouting party - but it's surely not the end of their mission.
Given that the movie Riot has Carnage's powers, it may be that Venom 2's Carnage will be another team leader: Kasady escapes from San Quentin and begins to hunt Eddie Brock before coming into contact with the more space-side of the universe. This brings two aspects of Venom - Eddie and the symbiote - together in the villain, and has enough story potential to perhaps build into a third film, possibly a Maximum Carnage-style event. It's a change-up from what's in the comics, but better fits the thrust of Sony's universe so far.
These are the two main possibilities, both of which take some liberties with the comic book canon. The second idea fits best with Riot's powerset in Venom, and indeed turns Riot into a sort of precursor to Carnage. As such, that's probably the strongest theory, but only time will tell which route Sony choose to take with Carnage in Venom 2.