I recently found a death record for a German-born ancestor who died in Pittsburgh, PA. On the record, it gives his parents' names as Joseph and Barbara. Since the ancestor was born in Germany, I'm assuming his parents were also German but that is not confirmed. It appears that his parents' names have been anglicized. Joseph was likely Josef or Jozef but what is the German equivalent of Barbara? Thanks for any assistance other researchers can offer.

Look here once, you find the explanation of the name Barbara and also Joseph:

http://www.behindthename.com/name/barbara

Thank you so much! You've been extremely helpful!

Bärbel (German)
is only a shortform in german, the "correct" is the same:
also Barbara
names orgin is at greek βάρβαρος, bárbaros „die Fremde/ the foreign“.
The St. Barbara's feast in the liturgy of the Catholic and the Greek Orthodox Church is since the 12th century the 4th December, which is popularly called Barbara-day.
Customs
According to an old tradition at St. Barbara branches of a fruit tree (usually from a cherry tree, an apple tree) or cut of a forsythia and put into the water. This Barbara Branches, in the Alps named Barbara-Tree, will bloom until Christmas Eve, and in the cold and dark winter time bring a little light into the apartment. This goes back to a single train of legend: On the way to the prison Barbara stayed with her ​​robe hanging on a branch. She put the broken branch in a container with water, and he flourished on the very day on which she was sentenced to death.
http://de.wikipedia.org/wiki/Barbara_von_Nikomedien
http://en.wikipedia.org/wiki/Saint_Barbara