And I do not mean "Jem'Hadar first", "Jem'Hadar second", and so on.
I mean these: Remata'Klan, Ikat'ika, Ixtana'Rax, Kudak'Etan
Jem'Hadar do not have parents, they are created in birthing chambers. I looked up a list of all the named Jem'Hadar characters and none appear to share the same name or part of it. There is only one Remata'Klan who's name end with 'Klan. Also while I write this it is very irritating putting the ' between the names everytime. So what's the ' for anyway?
While you call every soldier under your command first, second, third and so on, why give them such unique names?
I can only come up with the following: First of all giving them numbers all the time, might resemble them too much like Borg drones. Second, stating that they are born within birthing chambers, I could guess that either the first part or the second part might be named after their birthing chamber. This would make Remata'Klan "brothers" with Remata' kling* or Yesler'Klan. (Both names I just made up.) During the early nineties there was a cartoon called Exosquad where humans created the Neo Sapiens, also from something that remebled birthing chambers. Those who were created in the same chamber were considers brothers.
Also since the Jem'Hadar were created by the Founders and the founders also enhanced the Vorta somewhere in history, can we assume the Jem'Hadar names are part of the founders language? "Remata" could mean "thunder" and "'Klan" could mean "strike"?