The Ungerecht name is a rare name, both in the U.S. and in Germany. Out of 2.7 million immigrants that arrived in the mid 1860's, the only Ungerechts were the six from our family (others have come at other times). Only one Ungerecht is on the Vietnam Memorial Wall, out of 58,000 servicemen and women, and he is one of ours. In Germany the name is only found right around Meiningen, in the Thuringian Forest of central Germany. (See this search of modern phone records: http://www.verwandt.de/karten/absolut/ungerecht.html).
There were two known Ungerecht families that emigrated to the U.S. from this area, but any link between them is not known at this time. The other family settled in Tennessee, with some members moving on to Texas.
The name in German translates to "unjust" or "unfair" ("recht" is related to the English "right", so literally it's related to unrighteous). This might be why it is rare. But rare is a good thing for a genealogist!
It was a common first name at the time (after John the Baptist). In fact, it was so common, males usually went by their second name instead. The exception is for people called Johannes, they generally had no second name. The J is pronounced as a Y (think of Johann Sebastian Bach, who, incidentally, grew up about 25 miles away in Eisenach).