I highly doubt that the Germans or Mikhail Kalashnikov ever called it an "assault rifle".
When the Germans developed what was originally called the MP-44, they pretended it was a submachine gun because Hitler had prohibited the development of new rifles. When it got out that it was actually a rifle and not a submachine gun, Hitler was so impressed by it, that he christened it the
Sturmgewehr, or the assault rifle. It is now mostly referred to as the Stg-44.
While it looks like an AK-47, Kalashnikov did not base it on the Stg-44. He was already designed what became the AK-47 before the Germans fielded the Stg-44. The Soviets used the Stg-44 as the basis for the SKS.