Kylo Ren hated FN-2187 for deserting the First Order. The realization that this traitor, who had escaped on his father’s ship and was now fighting alongside Han Solo and his mother’s Resistance with his grandfather’s lightsaber must have enraged him to no end. FN-2187 was part of the First Order from near birth. Kylo had joined much later in life. FN-2187 must have seemed like a warped reflection of Ben Solo. Ren had killed Ben once, and likely felt great satisfaction at the prospect of doing it again.
FN-2187 slowly woke from the First Order’s mental conditioning and made a choice. The people who had taken him from his family, stripped him of his identity and formed him into a weapon were not going to make him into a murderer. A captured Resistance fighter was his way out. When Poe was gone, Finn started running and never really stopped.
Finn had been too scared to take on the first order, knowing just how powerful of a force they are. In the beginning of The Last Jedi, Rose Tico convinces Finn that he has no place left to run. He takes ownership of what the First Rrder did to him, he takes all his skills and training and wields them at the First Order to tear them down and destroy them.
Rose sees how far he is willing to go to destroy the First Order and realizes that he is walking a path of self destruction. At great risk to herself, she intervenes and stops Finn from making the biggest mistake of his life. Then she says something to him:
“That’s how we’re going to win. Not fighting what we hate. Saving what we love.”
-Rose Tico, Star Wars VIII The Last Jedi
With these words Rose Tico finished what Kylo Ren started: she killed FN-2187. Poe may have given Finn a name, but Rose gave him something more; something to fight for, a reason to live and keep on living.