Prabhupada's lecture - Śrīmad-Bhāgavatam 1.5.24 - Vṛndāvana, August 5, 1975
So (reading), "Such vedānta-vādīs or the bhaktivedāntas are impartial in distributing..." This Bhaktivedanta title was given on this vedānta-vādī because in our society there was no Vedānta. So some of the Vaiṣṇavas selected me to get this title Bhaktivedanta. Vedānta means bhakti, understanding bhakti. Because vedaiś ca sarvair aham eva vedyaḥ [Bg. 15.15]. So who can understand Kṛṣṇa unless he has bhakti? So this is the bhaktivedānta. So (reading) "Vedānta-vādī or the bhaktivedāntas are impartial in distributing the transcendental knowledge or devotional service. To them no one is enemy or friend, no one is educated or uneducated, no one is specially favorable, and no one is unfavorable. The bhaktivedāntas see the people in general are wasting time in false sensuous things.
Their business is to get the ignorant mass of people to reestablish the lost relationship with the prayojana, lost relationship with the Personality of Godhead. By such endeavor even the most forgotten soul is roused up to the sense of spiritual life, and thus being initiated by the bhaktivedāntas the people in general gradually progress on the path of transcendental realization. So the vedānta-vādīs initiated the boy even before he became self-controlled and was detached from the childish sporting, etc. But before the initiation, he (the boy) became more and more advanced in discipline, which is very essential for one who wishes to make progress in the line. In the system of varṇāśrama-dharma, which is the beginning of actual life, small boys, five years of age, are sent to become brahmacārī at the guru's āśrama just to learn discipline."