This pattern continued with imperialist Britain and Russia, while Iran remained continually the internal term.
1935 was a year of great reforms in Iran (the veil was abolished, men were ordered to wear Western dress, the language was cleaned of arabisms, Ferdowsi the author of "Shahname", where BTW Iran was the name used, was celebrated the year before) and the Shah decided that in order to shed of the past of being a semi-colony of Britain and Russia, "Persia" was only to be used to describe the inglorious past of weakness, while the hitherto internal term "Iran" was to be used also by the outside to mark a new beginning.
After studying primary sources, I stumbled upon the memoirs (published in the 1950's) of Wipert von Bluecher, the German ambassador to Persia from 1932-1935. He and Reza Shah hated each other, because the Germans back then were involved in numerous scandals in Iran. Bluecher makes many accusations against Reza Shah in his memoirs. He seems to be the primary source of the rumor that "Iran" was chosen to please the Germans. His "source" reveals the reliability of that claim: Allegedly he heard after the war from an unnamed friend that the suggestion of renaming the country internationally came from the Persian embassy in Berlin.
Given that... I think the official Iranian reason given above is more veritable than von Bluechers rumor.