Freeing or killing the Dane in AC Valhalla each comes with a different set of consequences for Eivor.
During the quest, "Uninvited Guests," in Assassin's Creed: Valhalla, Eivor is tasked with protecting the settlement of Ravensthorpe from the invading Danes of East Anglia. Players can prompt this quest by uncovering that region of the map. The actual battle takes place after the banquet scene immediately following that nasty conversation with Dag. Upon killing the invaders, Eivor gets to make the choice on whether to kill a captured Dane to send a message to their countrymen or to let them go free.
Free or Kill the Dane AC Valhalla
Here's what happens if the player chooses whether to execute or free the captured Dane from the quest.
Choosing to kill the Dane will upset Randvi. Obviously, it's not that Randvi cares much about the Dane's life. She was simply hoping to send spies after him and hopefully either uncover the location of more invaders or get some undercover intel. It doesn't really bear a consequence on Eivor's relationship with her, however. It's just a minor frustration.
Choosing the let the Dane free will greatly upset Dag. After the unfortunate conversation with him earlier, Dag will completely ignore Eivor's input and kill the Dane, himself. Additionally, this will put even more strain on the relationship between Dag and Eivor—but it will make Randvi happy as she can put her plan into motion.
Either way, the Dane ends up dead, so there really is no large consequence.