Finn progresses from a character actively running from and hiding from his past, aware of the evil his former employers are capable of and wanting nothing to do with being with or fighting against them. He is only interested in saving himself and Rey. As he grows, he decides that fighting for the bigger cause is a better way to live (and possibly die).
At the close of the events of The Force Awakens and the beginning of The Last Jedi Finn is still figuring out who he is:
He states to Poe:
"Look, Poe," he said. "I believe in what you guys are doing. But I
didn't join this army - I followed Rey here. I just don't want you
thinking I'm something I'm not."
Finn initially has no interest in being a hero. He wants to run away as far as he can:
"His friend's reaction only made Finn feel more guilty. Poe didn't
understand that Finn hadn't joined the attack on StarKiller Base to
help the Resistance, but to rescue Rey. Finn had dreamed of convincing
her to join him somewhere in the wilds of the Outer Rim, where the
First Order could never find them."
Finn is terrified of the First Order and only intent on being with Rey:
"Finn got to his feet. He knew what he had to do, [leave the
Resistance ship and go find Rey], even though Poe and his other
friends in the Resistance would never understand. He just hoped he
wouldn't regret it for the rest of his life."
When Rose confronts him (after stunning him for apparently deserting):
"Sorry," Finn said. "But I did what I did to help my friend, not to
join another army....'Look,' Finn said pleadingly, 'If I could save Rey by saving the Resistance fleet I would, but I can't. Nobody can."
Finn never cared about the First Order's cause, nor the Resistances' ideology (though he does agree w/ the later, just not enough to fight for it):
"'I was raised in an army to fight for a cause', he said. 'Then I met
Rey. And for the first time I had someone I cared about to fight for.
That's who I wanted to be."
He finally comes around to the realization, after seeing the nihilistic outlook of DJ, that there are bigger things worth fighting for rather than only looking out for yourself:
"You could pretend the regime didn't exist, or rationalize its
excesses away, or seek to insulate yourself through wealth or
connections, or flee it and hide*...all of those things were easy to
do. The harder thing by far was to fight - to attract that murderous
regimes attention, and become an object of it's malice. **But that was
the only thing to do. Those who chose something else were hoping that
the monster they had ignored would eat them last.
Fin had fought. It had taken him a while to understand that running
wasn't an answer, but he had figured it out. He had fought to save
Rey, at first, but Poe had been right - this was far larger than one
person, or two, or two billion. He hadn't won - that was an annoying
detail...and here at the end, he found he wouldn't trade having fought
and lost for being DJ.
Which leads him from being a man running away to save himself to being a man willing to sacrifice himself to save his friends in a suicide run to destroy the First Order canon:
"I won't let them win!, Finn said, his voice wild.