Nārāyaṇa — who abides in all beings
The Bhāgavata's first verse begins with 'Nārāyaṇa'—the one who abides in all beings (nāra = beings, ayana = abode); the entire Bhāgavata is a commentary on this one name.
नारायणो मधुपतिर्माधवो दोषवर्जितः ।गोविन्दः पुण्डरीकाक्षो विष्णुश्च मधुसूदनः॥
nārāyaṇō madhupatirmādhavō dōṣavarjitaḥ ·gōvindaḥ puṇḍarīkākṣō viṣṇuścha madhusūdanaḥ
Nārāyaṇa — who abides in all beings
The Bhāgavata's first verse begins with 'Nārāyaṇa'—the one who abides in all beings (nāra = beings, ayana = abode); the entire Bhāgavata is a commentary on this one name.
lord of Madhu, or: lord of sweetness
Mādhava — of the spring, the honey-one, of the Mādhava clan
This name appears in the gods' Milk Ocean hymn: 'O Mādhava—you who arose from the spring (mādhava), or who belong to the Mādhava clan, or who are the lord of Śrī (Lakṣmī whose husband is spring itself)'.
free of all fault or blemish
Govinda — finder of cows, of earth, of the Vedas
Indra performs the Govindābhiṣeka after the Govardhana episode: 'You protect (vinda) the cows (go) and the earth (go = earth) and the Vedas (go = Veda)'; the triple meaning is explained in Brahmā's narration.
lotus-eyed
Viṣṇu — the all-pervading
Viṣṇu ('the all-pervading') is the primary name of the Lord's manifestation of preservation; Kṛṣṇa identifies himself as the complete form of which Viṣṇu is one aspect.
the slayer of Madhu
The name recalls Kṛṣṇa's earlier incarnation as Viṣṇu who killed the demon Madhu in the primordial ocean; S.B.G 8 has an extended account; Arjuna uses this name when first asking Kṛṣṇa to speak in the Gītā.