Damodar also spelled “Damodara” & “Damodarah” is the 367th name of Vishnu from the Vishnu sahasranama. The various meanings of the name are given as follows:
The Lord when He was tied with a cord (daama) around His waist (udara), denoting a divine pastime in which Krishna’s mother devi Yashoda bound Krishna for being mischievous.
One who is known through a mind which is purified (Udara) by means of self-control(dama).
One in whose bosom rests the entire universe.