Despite being a native English speaker, I'm much more familiar with the abbreviations BRD and DDR than with FRG and GDR. This is probably because in English usage in all but the most official contexts, the standard forms for the two countries were "West Germany" and "East Germany". DDR nevertheless had/has a certain level of currency in English-language contexts, even where it can be expected that readers would not know what it stood for, while FRG is in my experience almost never encountered in the same circumstances.
These days in Sweden, the Federal Republic is sometimes officially referred to as "Förbundsrepubliken Tyskland" and Angela Merkel is routinely described as "Förbundskanslern". But I have never seen "Tyska demokratiska republiken" or "Demokratiska republiken Tyskland" or any abbreviation thereof. I don't even know whether either or neither of those is actually the correct form. In Swedish the DDR is always "Östtyskland" and the abbreviation always "DDR".