Kṛṣṇa is Para-brahman. Brahman, we are all Brahman, because we are part and parcels of Para-brahman. But we are not Para-brahman. We are subordinate Brahman. Eko bahūnāṁ vidadhāti kāmān (Kaṭha Upaniṣad 2.2.13). We are supported by Kṛṣṇa. We are supported by God. He is one. God is one. And the supported Brahmans, or living entities, they are innumerable, beyond the numerical strength. Asaṅkhyam. Nobody can count how many living entities are there, but God is one.
So from the ancient literature we understand that kṛṣṇas tu bhagavān svayam (SB 1.3.28). There are many incarnation of Kṛṣṇa, expansion of Kṛṣṇa, svāṁśa and vibhinnāṁśa. Some of the expansions are direct personal expansions, just like Lord Rāma, Nṛsiṁha-deva, Varāha. There are many. Rāmādi-mūrtiṣu kalā-niyamena tiṣṭhan (Bs. 5.39). Kṛṣṇa is existing, expanding Himself in various forms like Rāma, Nṛsiṁha, Varāha, and so many others.
There are different kinds of incarnations, avatāras—śaktyāveśāvatāra, guṇāvatāra, manvantarāvatāra, yugāvatāra. Many incarnations. And in the Bhāgavata it is concluded that the Lord's incarnations are so numerous that you cannot count. Just like if you sit down on the bank of a river, you cannot keep an account of the waves, how many waves are passing, similarly, there is no account how many incarnations are coming out from Kṛṣṇa. But Kṛṣṇa is above all.
Here Kṛṣṇa personally says, and it is confirmed by all the sages, authorities, formerly by great sages like Nārada Muni, Vyāsadeva, Asita, Devala, and in the modern age by all the ācāryas: Śaṅkarācārya, Madhvācārya Rāmānujācārya, Viṣṇu Svāmī—so many other ācāryas—Lord Caitanya. Everyone accepts that Kṛṣṇa is the Supreme Personality of Godhead. How can . . . (indistinct) . . . you deny? We have to be guided by the ācāryas. Ācāryavān puruṣo veda (Chāndogya Upaniṣad 6.14.2). One who follows the principles of ācārya, he knows the things as they are. That is the verdict.
In the Bhagavad-gītā also, you find: ācāryopāsanam (BG 13.8). We have to follow the footprints, footsteps, of the ācāryas, because they can give us right direction. And one who does not follow the ācāryas and creates and manufactures his mental concoction, his version will not be accepted.
There are many different commentaries on the Bhagavad-gītā, but not all of them are according to the direction of the ācāryas. You have to accept Bhagavad-gītā as it is, under the direction of the ācāryas. They do not make any change. They explain how Kṛṣṇa is the greatest, not that comment in a different way and deviate you that Kṛṣṇa is ordinary man.
So Kṛṣṇa, from Kṛṣṇa, the next expansion is Baladeva, svayaṁ prakāśa. And from Baladeva, there is catur-vyūha: Saṅkarṣaṇa, Aniruddha, Pradyumna. So again there is, from Saṅkarṣaṇa, there is Nārāyaṇa. From Nārāyaṇa, there is another expansion, the same: Saṅkarṣaṇa, Pradyumna, Aniruddha. And from that Saṅkarṣaṇa, there is puruṣāvatāra, Mahā-Viṣṇu. From Mahā-Viṣṇu, there is Garbhodakaśāyī Viṣṇu. From Garbhodakaśāyī Viṣṇu, there is Kṣīrodakaśāyī Viṣṇu. The Kṣīrodakaśāyī Viṣṇu is situated in everyone's heart. Īśvaraḥ sarva-bhūtānāṁ hṛd-deśe 'rjuna tiṣṭhati (BG 18.61).
In this way, Kṛṣṇa is expanding in so many ways: by personal expansion, by the expansion of His energy, by the expansion of His differentiated parts and parcels. Just like we are. We are, we living entities, are vibhinnāṁśa. We are also expansions of Kṛṣṇa. So He is expanding Himself in so many ways: svāṁśa, vibhinnāṁśa and śakti, taṭasthā-śakti, cit-śakti, antaraṅga-śakti, bahiraṅga-śakti. So we have to understand Kṛṣṇa in that way.
And if we study scrutinizingly all this literature, we shall come to the conclusion that Kṛṣṇa is the Supreme Personality of Godhead. And if there is any name of God, that is perfectly given in this word Kṛṣṇa, "all-attractive." There are many derivative meaning of Kṛṣṇa given by the ācāryas, but on the whole, Kṛṣṇa is the actual name of God.