The Ten Names
Adi Shankaracharya (8th century CE) organized monks into into ten orders (dasa=ten, nami=names). Many, possibly most, although not all swamis are related to one of these. Each related to common characteristics of the monks of each of the orders, as it was at that time. In the past 1200 years, however, there is not such a close relationship to the underlying meaning of the name. For example, it may have been true at one time that the monks of the Puri order "lived in the cities", although that is not a requirement, and swamis today of Puri dasnami live any a diversity of locations, some in cities, and some not. The relation to the name is nominal, at best.
Swami Rama writes in Living with the Himalayan Masters: "Our tradition is Bharati. Bha means 'knowledge'; rati means 'lover.' Bharati means 'he who is the lover of knowledge.' From this comes the word Bharata, the land of spiritual knowledge, one of the Sanskrit names used for India." Swami Rama's linkage to Bharati comes from his initiation as Dandi (staff carrying) swami, which was given to him by a leader of swamis who was of the Bharati order. At that time Swami Rama became known as Dandi Swami Sadashiva Bharati. It was much later that he took the name Swami Rama.
Bharati: full of light
Giri: live in the mountains
Puri: live in the cities
Van: live in forests
Aranya: live in groves
Tirtha: live in pilgrimage places
Parvat: live in the high mountains
Sagar: live at the ocean
Nath: defenders of the faith