Monk names usually come from the culture of their monastery. Many orders in the default settings draw on real-world monastic traditions, so names often reflect a specific heritage — but a monk can be any race, so their people are the natural starting point.
It’s also common for a monk to take a new name on taking their vows — sometimes a single evocative word tied to a virtue, an element, or a lesson of their discipline. A quiet, meaningful name suits the reflective, self-mastered feel of the class.