"Bundesrepublik Deutschland" is the official name of Germany since 1949. The part that was East Germany when Germany was divided, was called "Deutsche Demokratische Republik". When GDR vanished into the FRG they, according to the FRG-constitution, "joined the territory of the FRG". So, to call Germany "Bundesrepublik Deutschland" is the equivalent of "Republique de France" or "Republica de Portugal".
From 1254 until 1806 Germany was part of the Holy Roman Empire, in German "Heiliges Römisches Reich". From 1806 to about 1815 some states that belonged to the HRE joined Napoleon and were united in the "Rheinbund", the "Confederation of the Rhine". From 1815 to 1866 there was the "Deutscher Bund", the "German Confederation. From 1866 to 1871 there was the "Norddeutscher Bund" - the "North German Confederation".
In 1871 was founded the "Deutsches Kaiserreich", the German Empire, which existed to the end of WW I. Between 1918 and 1933 there was the "Weimarer Republik", the "Weimar Republic", which ended on 30 Jan 1933, when Hitler seized the power.
The time when Hitler was on power is in Germany nowadays called "Das dritte Reich", officially it was "Deutsches Reich". In English you call that time "Nazi Germany", officially it was (probably) the "German Reich".
After WWII, Germany's borders were defined as the borders from 1937. This area was then seperated between the four allied powers (USA, UK, France and USSR). In 1949, there were adopted two different constitutions, one for the zones of USA, UK and France (aka West Germany) on 23 May 1949, and one for the Soviet zone of East Germany on 7 Oct 1949.
P.S. I couldn't have done it without Wikipedia. The English articles are very good as well. Who wants to know more, please go over there.