According to this cyclingnews.com article, the Trek Madone was named by Lance Armstrong
Lance actually named the bike himself after the Col de la Madone in Menton, France, where Armstrong tested himself in training. “The Col de la Madone is a 12km climb that starts in the French village of Menton. It rises from close to sea level to 927 meters. Cyclists have long used it to test themselves. Having lived in Nice for four years, I rode it many times as well. The record of 31:30 stood for many years, until in 1999 when I broke it with a 30:47. For me, the Madone is the ultimate test. It always tells me if I’m ready – ready to ride fast and ultimately, win the Tour de France. It never fails.”
One visual part of the bike I like is how the top tube flares where it meets the head tube. I’m also glad the Madone doesn’t have a compact frame style so that it’s easy to fit two large water bottles in my small 50 cm frame. Madone is also not to be confused with the word “madrone” which is a type of tree.