If the student doesn't have a relationship with the monastic teacher and the ceremony is a public one with a congregation present, their new name will tend to reflect the lineage/tradition rather than the individual person. When it is given by a monastic who knows the disciple, however, the name is often tailor-made. Dharma names are generally given in the language of the particular sangha where the name is bestowed. People in the Karma Kagyu tradition of Tibetan Buddhism are often given the name Karma.