The player can become Thane in all of Skyrim's holds. Though if doing the civil war, it is best to hold off on becoming thane until your civil war faction controls the hold in question. Eastmarch, for example, the player can only get permission to buy Hjerim after doing "Blood on the Ice" and winning the Civil War for the Empire or doing "Blood on the Ice" and giving Ulfric the Jagged Crown for the Stormcloaks. There are required quests (including favors for the Jarl) and the usual doing favors for people in the hold. Major holds the player needs to do 5 such favors, minor holds (eg. Hjaalmarch) three favors.
