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On December 24, Yeltsin informed the Secretary-General of the United Nations that by agreement of the member states of the CIS Russian Federation would assume the membership of the Soviet Union in all UN organs (including permanent membership in the UN Security Council). Thus, Russia is considered to be an original member of the UN (since October 24, 1945) along with Ukraine (Ukrainian SSR) and Belarus (Byelorussian SSR). On December 25—just hours after Gorbachev resigned as president of the Soviet Union—the Russian SFSR was renamed the Russian Federation (Russia), reflecting that it was now a sovereign state with Yeltsin assuming the Presidency. The change was originally published on January 6, 1992 (Rossiyskaya Gazeta). According to law, during 1992, it was allowed to use the old name of the RSFSR for official business (forms, seals and stamps). The Russian Federation's Constitution (Fundamental Law) of 1978, though with the 1991–1992 Amendements, remained in effect until the 1993 Russian constitutional crisis.

What was the new name given to the Russian SFSR after the resignation of Gorbachev?
the Russian Federation