You contradict yourself there, since Martok's father was certainly far less prominent than Worf's.
But would the House of Martok exist before Martok himself rose to prominence (i.e. became Gowron's closest aide, even if that was really his Founder Doppelgänger)? In terms of canon evidence, that is. If not, then there's no contradiction.
Martok said he came from humble origins, not being a nobleman by birth and all. But he achieved high status nevertheless - perhaps through his heroic deeds, perhaps through the marriage where he seems to defer to his wife quite a bit. Surely this man, formerly lamenting his lack of status, would now create that status by creating the House of Martok?
I believe it is established that Martok was born a commoner, and so is the first head of House Martok, but I cannot find the reference.
The stuff about him being born commoner was given in "Once More Unto the Breach" where the nobleman Kor despised him for that. The idea that he would be the first head is just conjecture, though, not mentioned in the episode dialogue.
Worf, son of Mogh, was of the House of Mogh, just as Duras, son of Ja'rod was of the House Duras.
There are some nuances to that. The idea of a "House of Mogh" first appears in DS9 "Sons of Mogh", where it's retconned into having existed prior to Worf and Kurn's fall from grace. In "Soldiers of the Empire", it's even given its own crest. TNG never acknowledged the existence of a House of Mogh, though.
These things seem surprisingly consistent, or at least lacking in major contradictions. Worf's father Mogh might well have been the first member of his bloodline to ascend to such a status that he'd have a House of his own. OTOH, there are at least two Worfs in that bloodline, so there could well be ancient Moghs there, too. Similarly, there are at least two Durases in the Duras bloodline, so probably Ja'rod merely was a run-of-the-mill member of a House named after a famous ancestor of his... And so was his villainy son.
So, it is clear that the names of the Houses sometimes change, but still unclear why.
Hmh? It seems to me that the only time the name of a House "changed" was when the male bloodline of the House was snuffed out and an outsider claimed the booty (the House of Quark thing). That is, one House ceased to exist and a new one was founded on the ruins. There was just some confusion as to who'd claim the booty - first it was Quark, but then it was changed to be Grilka, by "special dispensation".
Perhaps females can't lead Houses at all. Or perhaps it's a revision of rules brought up by Gowron, who also seems to have removed the previously existing right of females to hold Council seats during his reign. It's difficult to tell since AFAIK we have only witnessed a single House name change, and we've never been explicitly told that another House would be named after a female, yet not been explicitly told one would
not be thus named, either.
Timo Saloniemi
