You'll see quite a few Japanese companies which have similar names to other ones due to the syllabic Japanese language (words are made up of syllables rather than distinct letters, so there are only so many combinations), or because they are named after their founding (and many people/places have similar names, also due to the syllabic nature). Both Aisin and Aisan get the first half of their name from the Aichi Prefecture (a Japanese province) they started in, it gets a bit complicated after that (Japanese is a strange language, you can have individual syllables that are pronounced one way but when combined with another are pronounced differently, so the San part of Aisan comes from Mie Prefecture (both san and mi are related to the number three). Aisin comes from when Aichi Kogyo (Aichi Industries) merged with Shinkawa Kogyo (Shinkawa Industries) to form Aisin Seiki (Aisin Standard, or something similar).
Another good example is that a lot of Toyotas will have Mitsuboshi (Three Stars) accessory belts, not to be confused with Mitsubishi (Three Diamonds)