Students of Japanese often get confused about when to use "Nihon" and when to use "Nippon" as the name of the country. In truth, there are many names for the "Land of the Rising Sun (a translation of Nihon / Nippon にほん / にっぽん / 日本), and sometimes the English name "Japan" gets thrown into the mix. All of these variants came together in an incident that is recounted for us by Jim Breen.
Ben Bullock (a Brit resident in Japan) remarked on the sci.lang.japan group recently that his local university library used "Nippon" instead of "Japan" for shelf labels, so it has "History of Nippon" and "Nipponese" for the language itself. All quite bizarre.
The discussion thread is here, and photos Ben took are here and here. I speculated it might have been a particular staff member at that library with a bee in his / her bonnet about the word "Japan" (which of course is not derived from any Japanese word), but Ben unearthed a 2012 bulletin from the "Japan Library Association" which says they are changing "Nippon" to "Japan". The bulletin is here and the passage is:
Nihon no yomi Ōbun hyōki tsuite
NDC 10-ban kara,`Nihon' no yomi wa `Nippon' kara `Nihon' ni henkō shi,
Ōbun hyōki ni tsuite `Nippon'`Nipponese' wa `Japan'`japanese' ni henkō suru.
Regarding the Latin letter notation of 日本:
Starting from the NDC10 version, the notation for the Latin letter reading of 「日本」will change from "Nippon" to "Nihon".
For European notation, "Nippon" and "Nipponese" will change to "Japan" and "Japanese".
So perhaps that "Nippon" usage is a bit more widespread. It certainly had some currency in library circles as they use / used it for their cataloguing standards, e.g.,
Nihon jisshin bunruihō「日本十進分類法」（Nippon Decimal Classification: NDC）
Nihon mokuroku kisoku「日本目録規則」（Nippon Cataloging Rules: NCR）
It appears in company names: NHK, NEC, etc. NHK is understandable – it's a contraction of the Japanese name (Nippon Housou Kyoukai). NEC as the public label of Nihon denki 日本電気 is a remnant – they changed the English version of their name to "NEC Corporation" 30 years ago, and even before then they avoided using "Nippon" in favour of just "NEC".
Nathan Hopson notes:
Nippon remains the preferred designation on the news, and is often somewhat self-consciously used on TV and radio to express a certain nationalist pride. As demonstrated by the use of "Nadeshiko Japan" (なでしこジャパン) and "Samurai Japan" (侍ジャパン) for the women's and men's national soccer team names, "Japan" is occasionally used in katakana transcription to mean "Japan as viewed from the outside world."
We may also observe that "Nippon~" is often used in Linnaean Latin names. People started to give scientific names to plants and animals in Latin in the 18th century, but in ancient Latin there was no word for Japan. Consequently, since Nippon is the original name for Japan, taxonomists felt free to use Nipponicus / Nipponia / Nipponicum when they named newly discovered plants and animals, and these names have been accepted by the scientific community.
[Thanks to Jim Unger and Hiroko Sherry]