CC Ādi 2.114
অসম্ভব নহে, সত্য বচন সবার ॥ ১১৪ ॥
asambhava nahe, satya vacana sabāra
Some say that Kṛṣṇa is the incarnation of Kṣīrodakaśāyī Viṣṇu. None of these statements is impossible; each is as correct as the others.
The Laghu-bhāgavatāmṛta (5.383) states:
mahendrānujatāṁ kecit kecit kṣīrābdhi-śāyitām
brūyuḥ kṛṣṇasya munayas tat-tad-vṛtty-anugāminaḥ
“According to the intimate relationships between Śrī Kṛṣṇa, the primeval Lord, and His devotees, the Purāṇas describe Him by various names. Sometimes He is called Nārāyaṇa; sometimes Upendra (Vāmana), the younger brother of Indra, King of heaven; and sometimes Kṣīrodakaśāyī Viṣṇu. Sometimes He is called the thousand-hooded Śeṣa Nāga, and sometimes the Lord of Vaikuṇṭha.”