Why the name? Because it sounds just like the US counterpart, Nuclear Regulatory Commission. (As if it's a good thing.)
The original idea for naming the new agency was to use the word "Safety" instead of "Regulatory". But the word "safety" has become such a dirty word in Japan over the last year (much like "hope" and "change" in the US over the past 3 years) the Noda administration, which seems to care very much (many say "only") about how it appears in the eyes of the international "community" (whoever that is), has decided not to use the word "safety" for the name of a new agency that will be created under the Ministry of the Environment (of all places).
From Asahi Shinbun digital version (1/24/2012):
The Noda administration informed the Democratic Party of Japan (DPJ, ruling party) on January 24 of its decision to name the new agency in charge of nuclear regulation "Nuclear Regulatory Agency". The agency will be set up as an affiliated agency to the Ministry of the Environment sometime in April.
The administration was going to name the agency as "Nuclear Safety Agency". However, the DPJ's project team on ending the nuclear accident requested last December to name it "Nuclear Regulatory Agency". The Nuclear Regulatory Agency will be created by separating out the Nuclear and Industrial Safety Agency from the Ministry of Economy, Trade and Industry, and combining the Nuclear Safety Commission under the Cabinet Office and the radiation monitoring division under the Ministry of Education and Science.