Answer
Krishna's name exists eternally. The holy name is not created at a particular point in time. Wherever Krishna exists, His name also exists eternally.
However, there is a special feature in Kali-yuga.
In previous yugas, the holy name could certainly be accessed, but one generally required a high degree of purity to fully contact the Lord through His name. The pure name would manifest on the tongue of a purified devotee.
In Kali-yuga, however, Krishna has specially invested His name with extraordinary mercy. This is the meaning of His appearance as the holy name. Even conditioned souls and sādhakas can begin chanting and receive purification.
The letters themselves are not the incarnation. Rather, Krishna has made Himself especially accessible through the chanting of His names.
In previous ages, one had to attain substantial purity before fully accessing the spiritual potency of the name. In Kali-yuga, the process works in a mercifully reversed manner. One chants even in an impure state, and through chanting gradually becomes purified.
That is the special concession of this age.
When we hear examples such as Ajāmila chanting "Nārāyana," we must remember that his situation was unique. Earlier in life he had been trained as a qualified brāhmana and had devotional impressions. The Lord never forgets the devotional service performed by His devotee. Therefore, special circumstances were present in his case.
The broader principle remains that Krishna has made Himself extraordinarily accessible through His holy name in Kali-yuga.
This is why we find the name of Krishna being spoken so freely and openly everywhere. In earlier ages and in the Vedic literature, Krishna's glories are certainly present, but often they are hidden, indirect, or revealed only to qualified seekers.
As Śrīla Prabhupāda explained, Krishna is mentioned throughout the Vedas and Upaniṣads as the Supreme Lord, but in Kali-yuga He has become especially available through the congregational chanting of His holy names.
This accessibility is one of the greatest mercies of the age.
