I quoted the first sentence of this section of Germany wikipedia page. It explains that Germany (Bundesrepublik Deutschland, BRD, West Germany) continued as the same state, not a new one, and as such kept all its existing links, including membership with EU.
East Germany was an actual state (German Democratic Republic, Deutsche Demokratische Republik) until the reunification with West Germany. “West Germany” and “Germany” designate the same state in different time periods.
I don’t think that it’s much worse that to say “West Germany”. In both case you are using an informal name, instead of the official country name.