This is kind of a short answer but there isn't really that much to say.

Capital and other large cities generally had (and sometimes still do) a German name. Like the now Slovenian capital city of Ljubljana (Laibach) or Pécs (Fünfkirchen) in Southern Hungary. Although a few didn't, most notably the Hungarian capital of Budapest. Tiny villages and such normally had just their one name unless they were in the transitioning zone to another language's area.

And lastly there's also the case of originally German cities in now non-German regions, like many parts of what is now the Czech Republic, most notably perhaps the heavily-German region of Silesia (like Šumvald, originally known as Schönwald). And of course Siebenbürgen (Transylvania), now residing in central Romania, which was (and to a small extend still is) an enclave of ethnic Germans since the Middle Ages with its own particular dialect (Transylvanian Saxon), centered around the cities of Brașov and Sibiu, which were originally founded as Kronstadt and Hermannstadt.

As reference here is a map depicting the ethnicities of Austria-Hungary according to the general census of 1880, made in Vienna in 1881 for the use of Germans.