The splitting of the word ‘Damodar’ gives us the meaning (dam- rope) and udar (belly). The other spellings of the word Damadar are Dāmodara and also Damodarah. Notably, this is the 367th name of Lord Vishnu in the Vishnu Sahasranam Stotram.
There are three meanings attributed to the name Damodar. The first one ensues from the story in Bhagavata which narrates Krishna’s divine play when he was tied to a wooden mortar with a rope by his foster mother Yashoda (dama – rope; waist – udara). The other lofty idea attached to the name means “The Lord who is known through a heart that is purified (udara) with the exercising of self-control (dama). The third interpretation says the word referring to “The Lord in whose bosom the entire universe rests”.
The story of Damodar mentioned in the Bhagavata Purana goes thus. Lord Krishna was known for his childhood pranks. With the complaints mounting up from the households of Gokul regarding little Krishna’s mischievous pranks, his foster mother Yashoda had no other choice than contemplating on restraining his movement. Therefore she wound a rope (dam) to a wooden mortar and tied it to Krishna’s waist (udar) and went to do her chores. Krishna being impatient of being confined to a place started moving about crawling on the streets with the wooden mortar rolling behind him on the move.
On the way, there stood two huge trees very close to each other. Krishna crawled in between the trees with the mortar getting stuck in between. When the little child effortlessly pulled the rope, the mortar got released by felling those huge trees with a thunderous noise. Two Gandharvas (celestial beings) who were the sons of Kubera (the god of wealth) emerged in their lustrous forms from the trees and bowed in front of Lord Krishna with folded hands. This was the day of redemption for them as they were mercifully rescued from their cursed state. Earlier, Sage Narad had cursed them for their arrogance confining them to the state of those two trees. Krishna’s divine touch had cured the curse and brought them out from their confinement.
Thus the divine name of Lord Krishna ‘Damodar’ reminds us of one of the most charming divine plays of the Lord.