When I was a kid, I came up with a theory that the jemhadar had no individual names, like the Borg. Everyone in a jem hadar unit was whatever prefix Remata or Omata etc refered to the name of the unit. Clan was added because they were all a cohort of a dozen or so people. And that the only way to distinguish amongst themselves was their rank, solidifying the whole “order brings victory, victory is life” mantra.

I know now that doesn’t really work but hey, I had fun thinking it up.