It is an ancient tradition that stemmed forth from the Vedic period that gave us the word ‘Namah’. In the passage of time, it came to be interpreted as prostrations or salutations, Namaskar.
In its virginal meaning, it was a term that came in vogue by the spoliation (lopa) of a term that is repeated very often in the Vedic rituals, as the pundits chant the mantras and offer the oblations to the sacred fire:
‘Agne Idam Na Mama’ “O Lord Fire! (This what I am offering is not mine’).
This term ‘Na Mama’ (not mine) expresses the mental attitude of the devotees; everything belongs to Thee O Lord – I am only offering to Thee what is already owned by You. This spirit of total dedication, complete surrender, and supreme selflessness is that which is expressed by the term ‘Na Mama.’
When this term came to be oft repeated by the mass of people the term got ‘defaced.’
This ‘Na Mama’ became ‘Nama’; the middle ma appears to have got lost in the stampede of centuries, in the cascade of general conversations.
Thus when we say ‘Krishnaya Tubhyam Nama’, we mean nothing is mine O Lord, everything is Thine and I thus totally surrender to Thee my beloved Sri Krishna.
(Source: Introduction section of Glory of Krishna published by Chinmaya Mission, Mumbai)