Bethesda has confirmed a few details about how Starfield player homes will work in a new fan Q&A. In short, you'll be able to purchase someplace to live in all major Starfield cities, and other options will be available if you complete certain questlines.
In a Q&A hosted on the official Bethesda Game Studios Discord, lead quest designer Will Shen explained that "there’s housing in different cities that the player can get. Some you have to purchase and some are rewards for specific quests."
