One possible encounter has a group of adventurers visit your tula. One option, in the grand tradition of adventurers everywhere, is to kill them and take their stuff. (This is sometimes described as the only right choice in the game.)
Orlanthi love cats and hate dogs, yet there's a group called the Wolf Tribe. Even if you maintain that dogs and wolves are separate creatures (which they aren't, but a primitive tribe may not know that), they're very similar regardless. Wolves also have a reputation for killing sheep and even cattle, particularly calves, if they get the chance to (a largely undeserved reputation, but a reputation nonetheless). Why would a cat-loving, cattle-centered people name themselves after a dog-like herd-killer?
Because wolves and dogs are considered aggressive and intimidating. The Orlanthi love cats and cattle, but even a Peace clan has to raid once in a while and the Orlanthi are, to the last man and often the last woman, a scrappin' folk. Naming your group after wolves and dogs is probably about on the same level as naming a sports team after the diamondback rattlesnake even though you'd never even consider keeping one for a pet.
Another possible randomly-generated name is the Grey Dogs, so while keeping dogs may not be cool, it's apparently okay to name yourself after them.
Some NPC clans also pointedly deviate from traditions followed by the player clan (one clan's chief deity is a troll god, for example, rather than Orlanth/Elmal/Ernalda) - preferring dogs over cats may just be another one of those differences.
Alternatively, it may be a sort of insult name. That is, perhaps the clan came from a group of people considered 'as bad as dogs' and, after surviving on their own, took a perverse pride in it and everyone else ended up mostly respecting them. Or perhaps, their local culture encourages a little ethical flexing. Or maybe their clan history simply involved some important event involving dogs.
There's an idiom in the tabletop version of the setting, "Orlanthi all", meaning six out of every seven and referring to how aggressively the Orlanthi differ from one another. "All" Orlanthi men worship Orlanth, but the seventh worships Humakt or Elmal or Issaries or even Eurmal. "All" Orlanthi women worship Ernalda, except for the seventh who worships Chalana Arroy or Ernalda. And "all" Orlanthi hate dogs and keep alynxes, but don't look at that seventh clan over there...
