Worf was accepted into the House of Martok at some point. The House of Mogh was no more.
Kor
Why couldn't Martok give back his name and honor at least?
Probably all the land and ships were given to other families. Okay. Wait...you know what? This doesn't make any sense.
Worf was under the assumption he had no family at one point. His parents killed. No one on Qo'Nos. So he was raised by humans. If he had relatives on the homeworld, surely he would have been raised by them, right? So if they had any land and ships back then, who owned them? Who was maintaining them?
Kurn is revealed to be his brother and they set about restoring their family's honor. It doesn't happen. But later, Worf and Kurn save Gowron's ass, and he has to restore their honor.
In that time, the House of Mogh has land and ships, that apparently Kurn runs, and Kurn even manages to get a seat on the high council.
So why couldn't Martok give Worf back his family name and honor. And on top of that, have Kurn work back up any accumulation of land and ships that would necessitate a successful house? If they wanted to do the honorable, selfless Klingon-without-a-home, great. It was already done though. If you're going to do a redux, make it worthwhile and not just some cheesy solution of, "hey Worf, I'll adopt you." I guess it was to show that Martok and him were true comrades. But it didn't feel substantial. I like shake ups but I don't think the pay off here was worth it. It'd be better if Worf had to endure as the shamed Klingon, but worse than what he went through on the Enterprise. What if he no longer had Starfleet either? That would be interesting.
Worf losing his family name was another bad development.