An interesting twist is that at least one school of Buddhism does not have monastics but does give Dharma names to lay followers at a ceremony called Affirmation. For example, from: http://bffct.org/bff/resources/shin-buddhism-in-a-nutshell/
In the Shin religion, there are no monastics, monks or nuns, but there are teachers both ordained clergy and certified lay instructors. They are not seen as above everyone else or holding the secret keys to spiritual liberation, but are ordinary people, both men and women, who are just more learned or experienced spiritual seekers.
In the particular American group referenced above, lay followers are invited to participate in an Affirmation ceremony upon completion of a number of requirements including general Buddhist studies and participation in a retreat. The lay follower selects their own Dharma name from a Zen tradition list such as:
The names range from lovely to self deprecating, which might be desirable for someone who wanted to keep the idea of humility close to heart.
I saw some scattered informal references to laity in Zen traditions receiving Dharma names (not sure of the extent of this practice) and even a mention of the deceased receiving a Dharma name in Japan:
In Japan, other than the standard usage of dharma names for monastics and laity, it is also tradition for the deceased to receive a dharma name (戒名, kaimyō; lit. "precept name") written in Kanji from the priest. This name supposedly prevents the return of the deceased if his name is called.