The information presented here will crop up in roleplay, but characters need not be aware of it.
Since kavkema are nomadic, scattered and frequently anti-natalist, groups of them are rarely encountered unless they've banded together into organisations with a purpose. There are a few larger organisations that are worth noting:
About a fifth or sixth of all wild kavkema identify with Shy͡ilun in some form. This organisation is the most 'successful' of the resistance movements, famous for training their members to withstand psychological warfare (though it's unclear if this has much of an effect). Their focus is on the rescue of kavkema, although they have historically unfortunately been just as likely to lose someone to the attempt as they are to free someone from the Nayabaru.
Shy͡ilun are gathered into shards - largely autonomous groups with a focus on the one or other task. One shard might be focussed on gathering intelligence and spreading it amongst other Shy͡ilun shards (lukiteva), another on the acquisition of resources (nhalteva), yet another on 'military' strikes (szateva).
The core of Shy͡ilun are adherents of the Akynkulla faith which, while not strictly incompatible with Tarnish, is very different to it. Tamas̈elu supposedly supports and de-facto leads Shy͡ilun.
They've claimed some of Tabraan for the kavkema, though knowledge of this has yet to proliferate through all of kavkem culture. The Tarnish kavkema don't know about this achievement.
Dynash is better understood as a set of beliefs or a collection of oaths than an actual organisation - there is no common leadership or even a common goal, other than sabotage and destruction of Nayabaru infrastructure.
About every tenth kavkem is Dynash, although unlike with Shy͡ilun, kavkema tend to be recruited to Dynash in whole groups, who often get to enjoy a few weeks of cult-like obsession.
Za'alseki are a medium-sized kavkem organisation predominantly based on Vatenas, where they are the main kavkem resistance movement. Their focus is less on rescue or destruction and more on finding novel ways to undermine Nayabaru attempts to control kavkema. They are generally patient and vindictive in their plans, and would rather spend weeks living undetected alongside the Nayabaru than actively destroy them.