The cities has got to be names the ruler have them, so the Hungarian cities should be German names because the Austrians gave them that names and they are the current ruler of it. also with Russian cities who there name changed in USSR, Stalingrad was Tsaritsyn.
But the Hungarian part of the Monarchy wasn't under Austrian rule, it was a Dual Monarchy where Hungary had the same rights as Austria. The common Ministries (foreign affairs, army, spendings) was under the control of both nations but Hugnary was totally free in her internal affairs had a separate government, etc.
http://en.wikipedia.org/wiki/Austria-Hungary