Both 'Nihon' and 'Nippon' are accepted in Japan. There is no regulation in Japanese constitution, nor in TV/Radio stations. Post Office decided to use Nippon for the stamps. You can say Nihon-jin, Nippon-jin for Japanese people. I think historically the old pronunciation of 日本 was something like 'Nit-phon', then it divided into 'Ni-hon' and 'Nit-pon(Nippon)'. Sometimes only one pronunciation is accepted. For example there are places called 日本橋 in Tokyo and Osaka. And 日本橋 in Tokyo should be called Nihon-bashi, 日本橋 in Osaka should be called Nippon-bashi. But this is just the local tradition.