"That was a different war. A different enemy." An enemy that's easier to fight, emotionally, because they're not human anymore. They're not ones who have chosen a different allegiance, or simply been born to a different allegiance. "If we win that battle, there's still another war to fight." Westeros is not great.

He stares into his ale mug for a moment. "There is no patriach anymore, not really. The only Stark male left will never have children of his own. I suppose I'm the closest thing -- the bannermen rallied around me for the fight."

That doesn't really explain why his name isn't Stark though.