The source of our family name is the small Polonia (now west Belorussia) town name.

In Polish Dworzec - means the railway station, the post station, the inn. I heard that in the 
Russian Empire officials gave family names - by the name of the place (where caught)
profession or even just on a whim.

So one of the versions - was caught at the station - they gave the name "Station." However, 
in Tel Aviv Museum of the Jewish diaspora gave me a computer version of the 
"small town in Poland." Subsequently, I found in three localities of Belarus with 
the same name (see section "History"). One of them mentioned in the Encyclopedic 
Dictionary of Brockhaus and Efron:

"The Dvorec (Dworzec) - a place of Grodno province, Slonim district, 39 miles
from the county town on the river Molchadka. Residents in 1108, orthodox church, church,
Jewish synagogue and house of worship, rural hospital, a distillery, 3 fairs. "