Another confusing case is the House of Martok: Worf describes it as having a highly honorable reputation, Martok's wife is even supposedly descended from an ancient Klingon princess, yet Martok himself is supposed to be a 'common soldier from the Ketha lowlands' with no noble blood. (I think that was the phrasing used)
I think that the house of Martok is a new one that begins with Martok. He was able through his own hard work to become a high ranking and well respected general which was enough to allow him to start his own noble house and pursue a noblewoman as his wife. Given how proud Sirella is she probably didnt even give him the time of day until after he had attained sufficient rank to be an acceptable suitor :P
Some Klingon great houses retain the name of the founder like the house of Duras (The Duras from TNG was the head of house of Duras but not the founder. He was named after the ancestor that founded the house i think) and the house of Mogh stays the same long after Mogh is dead and his sons with very different names are all that remain whilst some Klingon houses seem to change name every time the head of house was replaced the prime example being the house of D'Ghor/Quark/Grilka.
The series wasnt very consistent when it came to this. My own theory is that whoever starts the house gets to name it and as long as one of their descendants is in charge the house name remains the same. However if a head of house dies without an heir the house name changes to that of the new head of house. Martok started the house so the house is called Martok and since Martok himself is a highly honorable man his house has that reputation also.
Btw there is a memory alpha page on the Klingon great houses that lets you know how many houses are allowed on the council and stuff
I imagine with Klingon politics how they are that houses are constantly shifting round in terms of power and influence. There are probably plenty of fledgling houses that rise up due to, for example, a warrior distinguishing themselves and attaining high rank but then only last a couple generations before falling again whilst the older houses that have been playing politics longer tend to retain their power and influence unless something really bad happens to dishonor them all.