In the beginning (i.e. 50s) it was called Deutsche Lufthansa. They lost the ensuing legal battle with the western Deutsche Lufthansa who was declared the legitimate successor of the original pre war Deutsche Luft Hansa.
From that time, they called themselves Interflug (IF). Their base was at Berlin-Schoenefeld (SXF). They company as such still exists but consists of only one employee; it´s basically an empty shell used to pay off IF´s debts and settle legal stuff still coming up from time to time.
Peter, as far as I know they had only two A310 which are now Konrad Adenauer (10+21) and Theodor Heuss (10+22), the "Air Force Ones", so to speak. The MRT(T)s (10+24 [Otto Lilienthal] and soon 10+25 [the name escpaes me]) came later from Lufthansa.