So apparently Kol is the leader of the House of Kor. So could the house be unrelated to the TOS Klingon?
Hm, first I've heard of this. The press packet image says Kol is the leader of the House of Kor. Did he name the House after his son? Or was his father also named Kor.
Klingon house naming conventions are rather odd, since we've met Worf's grandfather, Colonel Worf, yet his house is the house of Mogh, Worf's father. So, a simple explanation is that Kor is an historic name for the house.
2 things to keep in mind 1) Just watch the show 2) These are like the costumes they give to people WAAAAY in the back of a scene because they will never be seen this close up :-)