Here, under the paragraph heading “FUJIFILM Holdings Corporation, Japan,” a commentator notes “Yes, the official name still has the word “film” in it…”
In Japan the word Fuji* is extremely common as a business name, usually appended somehow with other words to help differentiate each company or corporation.
Click on this kanji 富士 to perform a google search and see how many hits you get. There should also be a box on the right side showing a list of corporate hits in whatever your OS language is set to. Note that Fujifilm comes out top in both sets.
‘Fuji’ also pops up in other contexts. For example, I live near a primary school called Fujimi sho gakko (富士見小学校, with the mi / 見 kanji meaning “see”). So, I guess basically, ‘place from where one can see Mt. Fuji.’ The term Fujimi is a quite common place name.
In winter, when the winds clear the sky, I can see Mt. Fuji very clearly and dramatically from several locations near my house. This despite the fact that it is rather a long way away. Once you see Mt. Fuji, it is easy to appreciate how it’s totally dominating visual presence must have strongly affected the Japanese psyche through the ages, and it becomes easy to understand how the name must be seen as quite an auspicious one for a company to have.
* incidentally, in Japanese Mt. Fuji is usually referred to as Fujisan. The kanji is 富士山. The kanji 山 means mountain and is often pronounced as yama. In this case though, it is typically given the alternative reading of san.