Actually, you wouldn't need the "na" unless it was something like "House of the MacDonald" which would be Taigh na Dhòmhnullach.

If it is to be "House of Kendricks", you would just use Taigh Kendricks. However, Kendricks isn't the Gaelic. Any idea what that would be?

You should ALSO put the Gaelic form of Kendrick into the Genitive after the "Taigh".