Simple, those cities WERE German. They were originally Slavic until about the 8th century, give or take, until Germanic kingdoms began expanding further east. You can see this in the name Breslau, as the suffix in name refers to the Slavic peoples, before the land became heavily Germanized in the 11th century. These lands, primarily Silesia, the Sudetenland and Pomerania became majority German during the formative years of the Holy Roman Empire (as did other lands conquered by the Teutons such as Prussia, which was formally Baltic), and remained that way until the rise of Nazi Germany (there were notable Slavic minorities especially in Silesia). After WWII, the allies divided Germany by the Oder river, giving the land east of the river to Poland and exiling a few million Germans from these lands, and resettling it with Poles from out east (primarily from the land Poland lost to the Soviets such as Vilnius). These cities today are now a part of Slavic countries with Slavic majorities, meaning they are going to use their Slavic names in English. They still however for the most part use their old names in German.
From English perspective these names are exonyms. Nowadays United Nations advices to stop officially using those exonyms that are falling out of use. Imagine you want to describe your location, so you check what is written on buildings and signs and end with the name that is used by locals. It's a natural process.
Other remarks:
Maps older than "old maps" you mentioned used Latin names that were dropped and replaced by names that more closely resembled names used by local populations.
There weren't many Polish sources to base old maps on. Map creators cannot go everywhere and they must base their work on existing documents. Most of which were written in French or German. Later they could use administrative names that were also given in German, even if the majority of the population weren't German.
Of course these examples are, if anything, unique for Eastern Europe in that they "only" have a German name and a Polish or Czech name.
For cities in more ethnically or linguistically mixed areas in Eastern Europe, a city can have far more names. Modern Lviv in Ukraine was Lvov under the Russians/Soviets, Lwow under the Polish, and Lemberg under the Austrians. Lithuanian Vilnius has gone by Polish Wilno, Russian Vilna, and Yiddish Vilne.
Of course it's not really that the names have changed - these cities have multiple names in multiple languages. What changed in all of these examples, plus the OP examples, was that the state controlling the city changed, and with it the official language, hence the map name change.