Heil Doenitz :/ (apologies to Mitchell and Webb).

More seriously, after Hitler's suicide the government of Germany (which was haphazard, chaotic, and controlled very little territory anywhere) was theoretically the "Flensburg Government" under Admiral Karl Doenitz. This government was primarily what was left of the German Armed Forces High Command (Oberkommando der Wehrmacht), and its representative, General Alfred Jodl (the Chief of Staff of the German Army) was the one who signed the instrument of surrender in Reims on May 7, 1945.

Otherwise, after the surrender the Flensburg government really only existed in the minds of its participants, who held a number of rather pointless meetings before being disbanded and arrested by the Allies on May 23. After that there wasn't a formal authority in Germany until the occupying powers assumed full governmental responsibility under the Berlin Declaration of June 5, 1945, and the establishment of the Allied Control Council on August 30. The ACC met until the Soviet representative walked out on March 30, 1948. The Western Allies ended up forming an Allied High Commission for the Western Germany (it operated before transferring sovereignty to the Federal Republic of Germany in 1955) and the Soviet occupying authorities handed over sovereignty to the German Democratic Republic in 1949. However, technically the occupation and full restoration of German sovereignty did not occur until the Treaty on the Final Settlement with Respect to Germany aka the "Two Plus Four" Treaty of 1990.

Anyway, more on the Flensburg government can be found in an answer by u/Ameisen.