The name Dawathang means the plain of the moon and is related to the shape of the locality which looks like the moon on the 14th day. Guru rinpoche is said to have given a prophecy regarding the holy medicinal spring which sprouts in the place and the place itself

First there was only a small chorten called Begor chorten and the place was called Begorthang.
The temple was built in 1954 by by Dasho Phuntsho Wangdu and Ashi Pelden from Lamey Gompa palace. They foolow an advice from the great Tibetan master Polo Khen Thubten Kunga Gyeltshen who said that the temple will benefit Buddhism in Bhutan and protect the doctrine against invaders.
The temple was given to their son, the 2nd Palpung Khyentse Rinpoche (19 ?-1998), also called Palri Khyentse or Lamey Gompa Khyentse, who had been recognized by the 16th Karmapa. He was a high reincarnate lama close to the Nyingma and Karma Kagyu lineage. The temple is now the property of Ani Chador Dolma, Palpung Khyentse Rinpoche’s wife.

Source: www.bhutanculturalatlas.com