From Śrī Babaji’s commentary on Anuccheda 96 of the Bhagavat Sandarbha:

Śrīmad Bhāgavatam was spoken by Bhagavān Śrī Kṛṣṇa and not by His expansion Nārāyaṇa or Garbhodakaśāyī Viṣṇu. Therefore, it is called Bhāgavatam. The derivational explanation of this great Purāṇa’s name can thus be explained in four different ways, as follows:

1. Bhagavatā proktam iti, it was spoken by Bhagavān.
2. Bhagavat-pratipādakam iti, its subject is Bhagavān.
3. Bhagavad-ākarṣakam iti, Bhagavān is attracted to one who hears or even desires to hear it.
4. Bhagavat-prema-prayojakam, its purpose (prayojana) is to bestow love for Bhagavān.