There are some householders (grihasthas) with the surnames like Giri, Puri, Van, Aranya etc. They have these titles that belong to the Dashanami sannyasis. What is the reason behind this and which varṇas would such individuals belong to?
Shankaracharya of Puri, Srimajjagadguru Svami Sri Nischalananda Sarasvatiji Maharaja, explains, as follows.
Those, who after becoming sannyasis, due to the will of Bhagavan, became householders and entered grihasthashrama, continue the use of the titles as surnames for their family lineage. This explains why you see grihasthas with such names too.
Earlier, the tradition was only for brahmins to take sannyasa. Over time, brahmins, kshatriyas, and vaishya – due to their ability to wear yajnopavita (sacred thread) and hence study the vedas, started taking sannyasa.
Therefore those grihasthas who have the Dashanami titles may be brahmin, kshatriya or vaishya.