Start with a biography of Jacob Boehme. One that's easy to access is Wikipedia:
http://en.wikipedia.org/wiki/Jakob_B%C3%B6hme
It says, "Böhme was born in March 8, 1575, at Alt Seidenberg (now a part of Sulików, Lower Silesian Voivodeship, Poland), a village near Görlitz in Upper Lusatia, a territory of the Holy Roman Empire. His father, George Wissen, was Lutheran, reasonably wealthy, but a peasant nonetheless."
Other biographies also say he was a son of George Wissen. The information was presumably taken from his christening record, but you'd have to verify that from the original record. Other sources say his father was Jacob.
It was common in this period for university students and scholars to adopt new, academic names. There were no rules governing the choice but you can generally discover the reason with a little effort. Notice that his mentor was Abraham Behem. That seems a promising lead.