I imagine one of the history lessons in First Order curriculum would go something like this:
The birth of the glorious Galactic Empire brought forth by our eternal leader Emperor Palpatine signified the dawn of the New Order and the end of the corrupt and impotent Old Republic. With Vader's Fist leading the Imperial March, we were the heralds of a new era, an era of order and peace.
But the Rebel scum wanted the Republic and democracy back, the very political institutions that failed the galaxy. They sowed the seeds of war and anarchy to destroy our hard-won peace and stability. They dared to strike at our beloved Emperor. And with their help, the traitorous Jedi finally succeeded in assassinating our eternal leader.
As we mourned the loss of our Emperor, the Rebels struck in our moment of grief, destroying our fleets and seizing our homes, establishing a New Republic every bit as corrupt as the old.
After the setback on Jakku, they demanded peace from us on their terms. Without the wise Emperor to lead them, the spineless cowards of the Ruling Council abandoned the New Order and submitted to the insurgents.
But not us. We, the leaders of the Imperial military, the executors of the New Order, refused to abandon the Emperor's vision. So we left the Empire which no longer stand by the values it was founded on. We came here, to the Unknown Regions, to rebuild and one day return to liberate the galaxy like the clone armies of old did.
We are not the New Republic. We are not the Galactic Empire of present times that abandoned us. We are the heirs of the New Order and thus of the true Empire of old. We...are the First Order.