The Japanese website Capa Camera Web published an interesting article on the origins of the Nikon name (Google translated text):
“Nikkor” is the abbreviation of the company name “Nikko (NIKKO)” plus “R”
Succeeded in trial production of “Anita”, camera lens prospect of manufacturing with the Japanese optical industry, the brand name of the lens in 1932 was defined as “NIKKOR (Nikkor)”. This name is the abbreviation of the company name “Nippon Kogaku Kogyo”, “Nikko = NIKKO”, plus the “R” that is often used at the end of the name of a photographic lens. The first product with the name “NIKKOR” was the aerial camera lens “Aero-NIKKOR” made in 1933.
Nikon camera name that may have been “Nikorette”
Nikon Kogyo started manufacturing cameras after the Pacific War. In 1946, while developing a small 35mm camera, the camera name was decided as “Nikon”. By adding “N” to the end of “NIKKO”, which is an abbreviation of Nippon Kogaku Kogyo, the brand name is masculine and has a good tone. The camera under development was tentatively called “Nikorette”, but it seems that it became “Nikon” because it was judged to be weak as a product name. The camera, tentatively called “Nikorette,” was released in 1948 as the 35mm rangefinder-linked camera “Nikon.” It will be called “Nikon I type” later to distinguish it from the successor camera. Rangefinder cameras starting with type I are called “S series”.
Read the full article at Capa Camera (translated). See also the Nikon history at nikon.com and camera-wiki.
Here is another quote from Nikon’s website:
Around 1946, there was a large demand for Japanese-made cameras. The demand was estimated to reach 170,000 pieces, mainly consisting of orders from CPO and planned reserves for collateral export in return for imported goods whici included food goods. On the other hand, the production capacity for camera manufacturering was not yet sufficient. Production capability could only meet one third of the demand.
In response to this situation, Nippon Kogaku decided to complete the product as early as possible.From the beginning, this small-sized camera had been designed with the tentative name of “Nikorette,” based on the abbreviation of Nippon Kogaku (“Nikko”) and adding “ette” to indicate “small-size.” However, the prevailing opinion was that it was a weak product name, and upon subsequent review it was agreed that “Nikon” would be the formal name. The name was based on “Nikko,” adding “N” at the end to make it sound better.