Q: Why Pressburg in German?
The Slovaks called the city Prešporok until the defeat of the Habsburg Empire in World War I. It was a Slovakized version of its German name Pressburg (which, in turn, may have been based on an old Slovak–Slavic personal name). Bratislava had a documented German majority for the last 300 years of the Habsburg Empire, almost certainly for centuries more: its Town Hall records started to shift from Latin to German in the 1370s, correspondence in their native language from Slovak villages began to appear in the 1430s, Hungarian documents started to show up around 1500. The Hungarians adopted a different name for Bratislava – Pozsony.
The city was given the name Bratislava when it was made capital of Slovakia in the newly created Czecho-Slovakia. The city council passed its resolution on the new name on 27 March 1919, the Ministry for Governing Slovakia formalized the change in its decree of 4 October 1919.
Source of Bratislava
The Slovak and Czech politicians called the city Bratislava (initially also Bratislav) as soon as the new country emerged, although the name had not been current among the Slovaks earlier. Versions of the fashioned name sometimes occurred in the writings of Slovak activists in the Habsburg Empire after Pavol Jozef Šafárik (Paul Joseph Schaffarik in his German publications) said in his influential Slavic Antiquities in 1837 that the name of Pressburg contained a German borrowing of an Old Slavic name. Slovak activists adapted his reconstruction and ended up with Bratislava and similar-sounding names for the city.
Linguists determined later that while Pressburg may indeed have come from an Old Slavic personal name, the personal name Šafárik proposed was wrong. The activists and then politicians retained Bratislava regardless, partly because it had already become traditional among them and partly because it sounded symbolic – it seemed to combine the words for "brother(hood)" and "Slav, glory, fame."
The Hungarian and German minorities that found themselves in the new Czecho-Slovakia in 1918 resented their lot. Their refusal to use the Slovak capital's new name in their own languages was among the ways to demonstrate that. Budapest, Vienna, and Berlin did likewise. The name Pressburg has since largely disappeared from the German press, it alternates with Bratislava in the Austrian press, while Hungary uses only Pozsony, including in government documents, but adds Bratislava to Pozsony on international road signs. The name Pozsony (followed by Bratislava in parentheses) is also used in the Hungarian-language textbooks published in Slovakia for its Hungarian minority schools.
Budapest's argument is that the European languages commonly use their own names for foreign cities, e.g., Vienna is called Bécs in Hungarian and Viedeň in Slovak, and that using Pozsony for the Slovak capital in Hungarian is another instance of the same.
Bratislava's name in other languages is largely a non-issue in Slovakia, but some contend that the city's name was not merely switched from German and Hungarian to Slovak in 1919. It received a new name that it never had in German, Hungarian, or Slovak. According to that argument, refusing to call Slovakia's capital Bratislava is an alienating gesture (akin to, e.g., a refusal to call the Turkish city on the Bosporus Istanbul or the Norwegian capital Oslo and adhering to Constantinople and Christiania instead) and that it implies expansive ambitions in Central Europe.