Pradyumna: Translation: "I offer my obeisances unto Lord Śrī Kṛṣṇa, son of Vasudeva, who is the supreme all-pervading Personality of Godhead. I meditate upon Him, the transcendent reality, who is the primeval cause of all causes, from whom all manifested universes arise, in whom they dwell, and by whom they are destroyed. I meditate upon that eternally effulgent Lord who is directly and indirectly conscious of all manifestations and yet is beyond them. It is He only who first imparted Vedic knowledge unto the heart of Brahmā, the first created being. Through Him this world, like a mirage, appears real even to great sages and demigods. Because of Him, the material universes, created by the three modes of nature, appear to be factual, although they are unreal. I meditate therefore upon Him, the Absolute Truth, who is eternally existent in His transcendental abode, and who is forever free of illusion." (SB 1.1.1)
Prabhupāda: Vyāsadeva is offering his obeisances unto the Supreme Lord, Kṛṣṇa. Oṁ namo bhagavate vāsudevāya. Bhagavate, "unto the Supreme Personality of Godhead, who is known as Vāsudeva." Vāsudeva means the son of Vasudeva. Even the leader of the impersonalists, namely Śaṅkarācārya, he has accepted that the Supreme Personality of Godhead appeared as the son of Vasudeva and Devakī. People may not misunderstand. Just like we give identification by giving the name of father, mother, similarly, Kṛṣṇa's identification is that He is son of Vasudeva or son of Nanda Mahārāja, friend of Śrīdāmā, Sudāmā, lover of Rādhārāṇī. In so many ways He has got hundreds of thousands of names.