Question: What is the significance of the mantra “om namo bhagavate vasudevaya” in relationship to the Srimad Bhagavatam? Why is it recited in the first verse of the literature, as well as the first verse spoken by Sukadeva Goswami. Why is it unto Vasudeva Krishna rather than Nanda-nandana Krishna?
Answer by Romapada Swami:
Manifestations of Krishna outside Vrindavan – like in Mathura, Dvaraka etc. – are plenary expansions of Svayam Bhagavan Krishna. Krishna who appears in Mathura as the son of Devaki is understood to be Vasudeva Krishna, one of the four `catur-vyuha’ expansions.
Oṁ namo bhagavate vāsudevāya means “I offer my respectful obeisances to Lord Vāsudeva, or Kṛṣṇa.”
Srila Prabhupada’s Lecture on SB 1.1.1 — Caracas, February 20, 1975: Nature has given us the opportunity now to enquire about the Absolute Truth. And what is that Absolute Truth? Because this is our only enquiry, that “What is the Absolute Truth, or the origin of everything?” Therefore, in the Śrīmad-Bhāgavatam, first of all the obeisances or the respect is offered to Vāsudeva. Oṁ namo bhagavate vāsudevāya means “I offer my respectful obeisances to Lord Vāsudeva, or Kṛṣṇa.” This Śrīmad-Bhāgavatam is being presented by Vyāsadeva, the most exalted personality, the guru, Vyāsa guru or Vedavyāsa, for all advanced spiritually conscious men. The spiritual master is called, therefore, representative of Vyāsa, Vyāsadeva. Therefore, on the birthday of spiritual master, it is said, Vyāsa-pūjā. So, this understanding, that Vāsudeva is the origin of everything, is available in human life.”
As far as your 2nd question, our acaryas explain how Vasudeva-Krishna transcendentally merged into the body of Yasoda-nandana Krishna, or Nanda-nandana Krishna, when Vasudeva brought Krishna to Vrindavana in the dead of the night. In other words, there is a feature of non-difference, when referring to either Vasudeva-Krishna and Nanda-nandana Krishna.