Jon Snow was a bastard. Even though he had mostly the same upbringing as his trueborn siblings, he never really paid much attention to the lessons with Maester Luwin, aside from the few topics that interested him. Maybe if you asked him about those Houses back in Winterfell, he would know. But after nearly six years, he forgot most of the Southern Houses, except maybe Houses Targaryen and Lannister and the more significant parts of history. He had a better recollection of Northern houses, but even those were half-forgotten in the rollercoaster that was his stint on the Wall. He honestly had no idea where Tarth was and knew nothing about House Payne.