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.
That could be the case here. Vic may be singing in Federation Standard (aka English) and Kira /Odo have learned it after hanging out with the Federation for the last six to seven years. Considering their backgrounds as people who lived in multi-lingual societies (from the Occupation), it wouldn't be the strangest thing for them to pick up a new language with some off screen effort over the years.
Is this what is thrown after a Gorn Wedding instead of Rice?