For its first 71 years, the company behind Nikon cameras was not called Nikon at all. It was Nippon Kogaku K.K., which means roughly "Japan Optical Company."
Nippon Kogaku was formed on 25 July 1917, when two Japanese optical businesses merged. Wikipedia gives either 25 or 26 July for the date. In its early years it built lenses and optical instruments, partly for the Japanese military. It did not sell a camera under its own name until the late 1940s.
The brand names came first. The company's lenses carried the name Nikkor from 1932. According to Wikipedia, Nikkor was a Westernized form of Nikko, which was itself an abbreviation of the company's name. Nikko is also a Japanese word that can mean "sunlight," and it is the name of a well-known hot-spring town. Neither of those meanings was the point. The name was simply a shortened Nippon Kogaku.
The step to Nikon happened in April 1946. The company was planning a compact 35mm camera and needed a name for it. Digital Camera World reports that the team considered "Nikorette" and rejected it as too weak. PetaPixel adds that the "-ette" was meant to signal a small camera. They kept the Nikko base and added an N. The reason given is that the extra letter gave "a more masculine impression in the Japanese language." Wikipedia describes the same change as Nikko gaining an extra "n." Neither source says who in the company made the final call, so the person behind the name is not recorded in what we found.
The first camera sold as a Nikon was the Nikon Model I, launched in 1948. The name then attached itself to the whole business. Nippon Kogaku officially became Nikon Corporation on 1 April 1988.
The name caused one legal snag. Wikipedia notes that it looked too close to "Ikon," a brand of the German firm Carl Zeiss. In Germany, the Nikon F was sold under the Nikkor name from 1963 to 1968.
So Nikon is a company name worn down twice: Nippon Kogaku became Nikko, and Nikko gained an N. The "Japan" and the "optical" are still in there, just hard to see.