In the booksEdit
In the A Song of Ice and Fire novels, House Kenning is a noble house who were once bitter foes of House Harlaw, but were defeated and are now their vassals. Their sigil is the Storm God's cloudy hand, pale grey, yellow lightning flashing from the fingertips, on black.
There's also a House Kenning in the Westerlands, seated at the castle of Kayce, located in a peninsula south of Fair Isle and northwest of Casterly Rock. House Kenning of Kayce is a cadet branch born in the days the ironborn held much of the Western coast of Westeros, from Bear Island to the Arbor. It was founded by Herrock Kenning who's warhorn (called the Horn of Herrock) has been passed down by his descendants. Eventually the Lannisters drove the ironborn completely out of the mainland (of the Westerlands), while House Kenning of Kayce stayed and accepted Lannister rule.
In real life, a "kenning" is a type of figurative device used in Old Norse poetry.
Houses from the Iron Islands