The Matterhorn is named after the grass at its feet, not the rock at its top.
Matterhorn joins two German words. Matte is a meadow or alpine pasture, and Horn is a horn. Wikipedia translates the whole as "the peak of the meadows" and dates the German name to 1682. Etymonline adds that the horn describes the shape, carved by Ice Age glaciers, while the meadows lie at the base.
The village below shares the root. Zermatt first appears as Zur Matte, "at the meadow." That form is not documented until a map of 1495 and a text of 1546, though it may be older. Even the village's older names, Praborno or Prato Borno, contain prato, another word for meadow.
German Matte has an English cousin. Etymonline traces it to Proto-Germanic *medwo, which also gave Old English mæd, the archaic English mead, "meadow."
The horn shape has become a technical term. Geographers call a peak carved by several glaciers a pyramidal peak, or in extreme cases a glacial horn. One with four symmetrical faces is simply called a Matterhorn.
On the Swiss-Italian border the mountain has a second name with a separate history. The French Cervin and Italian Cervino descend from the Latin Mons Silvanus, from silva, "forest." Over time that wore down to Selvin and then Servin. The naturalist Horace-Bénédict de Saussure is credited with changing the "s" to a "c," because he thought the name was linked to deer, French cerf and Italian cervo.
The Latin name has its own puzzle. A map of 1545 labels the mountain Mons Silvius, and Etymonline says that name may come from a personal name. In 1574 Josias Simler suggested Silvius was a Roman leader, and later writers repeated the idea.
Locals had plainer words. Speakers in the Aosta Valley call it Gran Bècca, "big mountain," and Walser-speaking locals simply say Horu. In German, though, the meadow has been part of the name since at least 1682.