There isn't actually such a thing as genocide-run Frisk. The idea is that the only reason Frisk gives their name to Asriel in the true ending is because that's their true nature; a pacifist. The genocide run is not done in any way with Frisk's consent, but is instead the Player forcing them to kill and see what happens. This combination of immense Determination and willingness to kill brings Chara's spirit back from nonexistence, who takes control of Frisk as the run progresses. This is why as the route goes on, "Frisk" will begin to take more and more actions without your input (i.e. approaching Papyrus at the end of Snowdin, attempting to attack Monster Kid, etc.).
At any point, should the Player stop forcing Frisk to kill and allow monsters to live, Chara will lose control. However, should the Player allow them control up until Sans, there's pretty much no turning back without resetting. After Chara approaches and strikes down Asgore and Flowey (with no input from the Player whatsoever), Chara will manifest on screen and speak directly to the Player, telling them that it was their Determination which brought them back from the dead. They also explain that they exist as a feeling in individuals whenever they choose to kill for personal gain, or simply no reason at all. They will then prompt the Player to destroy the world, as there is now nothing left for them, so they can move onto the next and continue killing, there. Should the Player comply, Chara will say they'll make an excellent partner before erasing the world. Should the player refuse, Chara will laugh, basically telling the Player they were never actually in control, then destroy the world, anyway.
When the Player tries to return to the game, they will find nothing but emptiness. If the Player waits for ten minutes(?) in that emptiness, Chara's presence will speak to them, questioning why they would want to return to the world they helped destroy, since it's basically all the Player's fault in the first place. However, they will offer to return the world if the Player gives up their SOUL to the demon. If the Player refuses, Chara will tell them that they can just stay here forever, forcing the Player to wait another ten minutes(?) to try again. When they finally accept, Chara is linked to the Player, allowing them full control of Frisk in all timelines, even after True Resets. The effects of this can be seen when certain characters will now get an odd, uncomfortable feeling around Frisk regardless of their current path, and in every subsequent true pacifist ending, the game will be altered to remind the Player that Chara is still very much in control, pushing even the happy ending to the worst outcome.
Hope this at least somewhat helped.