I'm just in the process of reading Brinkmanship
now, and I agree that the Tzenkethi have quietly become the most interesting part of the Typhon Pact - both the books and the fictional entity. The insight we've got into the Breen, Gorn and Kinshaya has been great, sure, (Romulans we already knew and were never very interesting in the first place, Tholians got their attention in the VAN books), but between the three authors who have developed them, the Tzenkethi have emerged as the most intriguing new culture, worming their way into every part of the astro-political situation. They have total unquestioned control over their own culture, and now that they're part of an alliance, they're more than willing to do their best to extend that control to the entire alliance.
I've occasionally had a bit of trouble nailing down the difference between the second and third parts of their names, though. The second particle is basically a caste, is that right? A level of society in which they exist, like a more rigid version of calling ourselves upper class or middle class, or the Bajoran d'jarra system. The third particle is their job within that caste, like having "Bob the working class labourer" as one's full name. Given that Tzenkethi are designed and tested and controlled to serve their one function in society for basically their whole lives with no deviation, it makes a certain amount of sense that their occupation would be written right into their name.