My daughter's seemingly simple question, "why is Fairmont High School named Fairmont", turned into a history hunt going back to the early 1900s. While I can't find a definitive reference to verify what I believe to be true, it seems very likely the following is the source.
The first Fairmont High School was a small four-room building that opened in the fall of 1906 and was located on Dorothy Lane just west of Far Hills Avenue. That area was named the "Fairmont Plat" (highlighted in the image below) back in those days, so it makes sense that's where the high school's name originated. Today, Fairmont Avenue is located in that same area.
Fairmont seems to be a name that references a good view from a high point and looking west from Fairmont Plat you would see down the steep hill to the valley that now stretches from Community Golf Course to the Great Miami River.
Fairmont High School is currently in its fourth location as population growth through the 1900s resulted in larger facilities being built. More details can be found at this link.
The entire map of Van Buren township, now the cities of Kettering and Moraine, and a peek into the names of its past, can be found at this link.