So many groups have sprung up under the generic title "Hare Krishna", but the origin of the Hare Krishna Movement was Srila Prabhupada (His Divine Grace A.C. Bhaktivedanta Swami) and his books. Since his departure in 1977, many people have deviated from that standard, so to distinguish ourselves, we call ourselves "the Bhaktivedantas", after His Divine Grace A.C. Bhaktivedanta Swami Prabhupada. Throughout history, even in the mundane world, people have taken the names of their founders to distinguish themselves from all the rest. So we have the Buddhists, who followed Lord Buddha, the Christians, who followed Jesus Christ, the Mohammedans, who followed Mohammed, the Franciscans, who followed St. Francis, the Lutherans, who followed Martin Luther, the Calvinists, who followed Calvin, the Marxists, who followed Marx, the Maoists, who followed Mao Tse Tung. By the name, everyone is put into his place. So we wish it to be known that we will follow Srila Prabhupada, His Divine Grace A.C. Bhaktivedanta Swami. This is our stand, and therefore we have assumed this name "the Bhaktivedantas", which can also be read as "the Bhaktivedanta's", meaning that we belong to the Bhaktivedanta Srila Prabhupada.
Srila Prabhupada himself suggested this name Bhaktivedantas:
Next January there will be an examination on this Bhagavad-gita. Papers will be sent by me to all centers, and those securing the minimum passing grade will be given the title as Bhakti-shastri. Similarly, another examination will be held on Lord Caitanya‚s Appearance Day in February, 1970 and it will be upon Srimad-Bhagavatam and Bhagavad-gita. Those passing will get the title of Bhakti-vaibhava. Another examination will be held sometimes in 1971 on the four books, Bhagavad-gita, Srimad-Bhagavatam, Teachings of Lord Chaitanya and Nectar of Devotion. One who will pass this examination will be awarded with the title of Bhaktivedanta. I want that all of my spiritual sons and daughters will inherit this title of Bhaktivedanta, so that the family transcendental diploma will continue through the generations. Those possessing the title of Bhaktivedanta will be allowed to initiate disciples. Maybe by 1975, all of my disciples will be allowed to initiate and increase the numbers of the generations. That is my program. So we should not simply publish these books for reading of outsiders, but our students must be well versed in all of our books so that we can be prepared to defeat all opposing parties in the matter of self-realization. [Letters from Srila Prabhupada, Letter to Hansadutta, 3 December 1968, Los Angeles (68-12-03)]
So [reading], "Such vedanta-vadis, or the bhaktivedantas, are impartial in distributing." This "Bhaktivedanta" title was given on this vedanta-vadi because in our Society [Gaudiya Math Society] there was no Vedanta. So some of the Vaishnavas selected me to get this title "Bhaktivedanta". Vedanta means bhakti, understanding bhakti. Because vedais cha sarvair aham eva vedyam. [Bhagavad-gita 15.15] So who can understand Krsna unless he has bhakti? So this is the bhaktivedanta. So [reading] "Vedanta-vadi, or the bhaktivedantas, 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 bhaktivedantas 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 bhaktivedantas, the people in general gradually progress on the path of transcendental realization. So the vedanta-vadis 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." [His Divine Grace A.C. Bhaktivedanta Swami Prabhupada, Srimad-Bhagavatam Lectures, Vrindavan, August 5, 1975, Srimad-Bhagavatam 1.5.24]