The Star Trek writers may very likely have made up the name "Jadzia Dax" for their character, but "Jadzia" also, coincidently, happens to be a real name in Poland. It's a form of "Jadwiga", which comes from the German name "Hedwig" meaning "strife-battle".
It wouldn't have been the first time the Trek writers selected a name for a supposed alien character, which also happened to be a genuine (and not too unusual), human-type name. When the character "Spock" was named for the original Trek series, the question was brought up at the time as to whether the writers had named him after the then-popular baby expert, Dr. Spock. The reply was that no-one on the Trek team had ever even heard of Dr. Spock.
Which kinda clues one in to the fact that the Star Trek *teevee* writers may not always have been completely aware of what was going on in the world around them.
I personally prefer the Trek novelists. ;)
-- Nanaea