There are 88 named mountain ranges in New Mexico.
For the Valles Caldera, the southwest and west are the Nacimiento Mountains-(Sierra Nacimien); the northwest of the caldera is the San Pedro Mountains, a redirect to the Nacimiento's. The rest of the Caldera, especially the south, east, northeast, and north is the Jemez Mountains. The north, descends to Abiquiu Lake, and the Chama River a northwest tributary to the Rio Grande. The north is also dotted with many peaks, or (cerros), some mesas, etc.
The Valles Caldera is located in central-north, and northeast Sandoval County and Los Alamos County. Eastern foothills are in extreme northwest Santa Fe County. The north of the Caldera is in southern Rio Arriba County. Thus the explanation for the three named mountain ranges around the Caldera.