What does “Krishna” mean?
The meaning is immediately evident to anyone who knows any of the thousands of śāstric statements like “The All-Attractive himself is Krishna” (kṛṣṇas tu bhagavān svayam). It is immediately clear to anyone who has been able to hear Krishna’s glories described by a realized paramparā. It is even immediately obvious to anyone who has heard about Krishna from countless conventional sources. As soon as we hear this name, “Krishna,” the object that immediately becomes manifest in our mind (i.e. the person, Krishna) is the primary meaning of the word. As soon as we pronounce even the first syllable of this name, “Krishna,” our minds immediately comprehend the direct and obvious meaning.
“Krishna: (1) His complexion is blue-black like the Tamāla tree, he is breast-fed by Yaśoda, and he is the Supreme Spiritual Substance.” — Nāma Kaumudī
“Viṣṇu, Nārāyaṇa, Kṛṣṇa, Vaikuṇṭha express the same meaning… Kṛṣṇa is Vasudeva’s son.” — Amara-kośa
“Kṛṣ is a word that means ‘existence.’ Ṇa means ‘carefree.’ Taken together, as Kṛṣṇa, they denote the Supreme Spiritual Substance.” — Gopāla-tāpanī Upaniṣada, Pūrva 1.1
[The above is translated from Tattva-Sandarbha 47.2. Amara Kośa and Gopāla-tāpanī references are given in the commentary of Śrī Satyanārāyaṇa dāsa Bābājī.]