It’s a more archaic-sounding term that GRRM probably picked to distinguish the Starks from the other old Kingdoms. There are other examples in history and folk lore of using “in” rather than “of”:
- between 1701-1772, the Hohenzollern were Kings “in” Prussia rather than “of” Prussia
- there’s the English concept of King (or Queen) in Parliament as the monarch-as-legislator.
- similarly in Sweden, the King in Council used to be the foremost executive authority.
- the Holy Roman Emperors also called themselves Kings in Germany after 1508,
- there’s the legendary sleeping King in the Mountain.
- there’s the King in Yellow by Chambers.
In terms of what it symbolizes, it could be a shortening from Only or True King in the North since at the beginning there were many kings in the North (such as the Barrow Kings who claimed to be descended from the First King). It could be a suggestion that the North cannot be owned and that the Starks stand as stewards of the land.
We’ll have to ask GRRM.
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