My grandfathers's parents were from Poland, and were born with a different name. They changed their name to Parecki after moving to Argentina. They left Poland for Argentina around 1910-1920.
Their name in Poland was Paretzki.
In Polish, adjectival names very often end in the suffixes -ski, -cki and -dzki, and are typically considered to be either typically Polish or typical for the Polish nobility.. It is more likely the name refers to nobility when the surname contains a name of a city or town.
Given this, it is likely that the name means "from Paretz" or "lord of Paretz".
There is even a Historical Society of Paretz which has a very nice web page, complete with frames: www.paretz-verein.de
Some highlights from their "Village History" page:
The name "Paretz" is of Wendish origin. The original name was "Porats" and came from the Slavic, "po reka" meaning "the river".
Paretz was mentioned for the first time in a deed of Markgrafen Otto II. von Brandenburg dated 28.05.1197. At that time there were two places called Porats: German-Porats (today Paretz) and Wendish-Porats, whose position today is no longer clearly identifiable.
So it would appear that ~1197 is the first occurence of the name "Paretz," and it was from a town in Germany. The Wendish Crusade was in 1147 and was led by the Kingdom of Germany against the Wends. It makes sense that the name is Wendish since the name came into existence after the crusade.
Now that we've found the origin of the name, we need to figure out how they got back to living in Poland.
By the 1600s, the Paretz Palace was already pretty solidly German, so I think we're looking for some Polish roots from before that time.
This is still a work in progress. I hope to continue this research at a later date!