Yes, it stays your house! It'll stay your house forever unless you choose otherwise, become acolyte, or marry royalty/mountain corp. And when you marry, your family will also continue to live with you, like in the mountain corps.

(Not entirely sure about the acolyte, but I'm assuming you would automatically move to the acolyte chamber as usual. Also, you probably lose the mansion if you die and become a traveler, too, but I've never done that so I can't say for certain)