The word aham indicates a person. As explained in the Vedas, nityo nityānāṁ cetanaś cetanānām (Kaṭha Upaniṣad 2.2.13): the Lord is the supreme eternal among innumerable eternals and the supreme living being among the innumerable living beings. The Lord is a person who also has impersonal features. As stated in Śrīmad-Bhāgavatam (1.2.11):

vadanti tat tattva-vidas
 tattvaṁ yaj jñānam advayam
brahmeti paramātmeti
 bhagavān iti śabdyate

“Learned transcendentalists who know the Absolute Truth call this nondual substance Brahman, Paramātmā or Bhagavān.” Consideration of the Paramātmā and impersonal Brahman arose after the creation; before the creation, only the Supreme Personality of Godhead existed. As firmly declared in Bhagavad-gītā (18.55), the Lord can be understood only by bhakti-yoga. The ultimate cause, the supreme cause of creation, is the Supreme Personality of Godhead, who can be understood only by bhakti-yoga. He cannot be understood by speculative philosophical research or by meditation, since all such processes came into existence after the material creation. The impersonal and localized conceptions of the Supreme Lord are more or less materially contaminated. The real spiritual process, therefore, is bhakti-yoga. As the Lord says, bhaktyā mām abhijānāti: “Only by devotional service can I be understood.” Before the creation, the Lord existed as a person, as indicated here by the word aham. When Prajāpati Dakṣa saw Him as a person, who was beautifully dressed and ornamented, he actually experienced the meaning of this word aham through devotional service.

Each person is eternal. Because the Lord says that He existed as a person before the creation (agre) and will also exist after the annihilation, the Lord is a person eternally. Śrīla Viśvanātha Cakravartī Ṭhākura therefore quotes these verses from Śrīmad-Bhāgavatam (10.9.13-14):

na cāntar na bahir yasya
 na pūrvaṁ nāpi cāparam
pūrvāparaṁ bahiś cāntar
 jagato yo jagac ca yaḥ

taṁ matvātmajam avyaktaṁ
 martya-liṅgam adhokṣajam
gopikolūkhale dāmnā
 babandha prākṛtaṁ yathā

The Personality of Godhead appeared in Vṛndāvana as the son of mother Yaśodā, who bound the Lord with rope just as an ordinary mother binds a material child. There are actually no divisions of external and internal for the form of the Supreme Personality of Godhead (sac-cid-ānanda-vigraha), but when He appears in His own form the unintelligent think Him an ordinary person. Avajānanti māṁ mūḍhā mānuṣīṁ tanum āśritam: although He comes in His own body, which never changes, mūḍhas, the unintelligent, think that the impersonal Brahman has assumed a material body to come in the form of a person. Ordinary living beings assume material bodies, but the Supreme Personality of Godhead does not. Since the Supreme Personality of Godhead is the supreme consciousness, it is stated herein that saṁjñāna-mātram, the original consciousness, Kṛṣṇa consciousness, was unmanifested before the creation, although the consciousness of the Supreme Personality of Godhead is the origin of everything. The Lord says in Bhagavad-gītā (2.12), “Never was there a time when I did not exist, nor you, nor all these kings; nor in the future shall any of us cease to be.” Thus the Lord’s person is the Absolute Truth in the past, present and future.

In this regard, Madhvācārya quotes two verses from the Matsya Purāṇa:

nānā-varṇo haris tv eko
 bahu-śīrṣa-bhujo rūpāt
āsīl laye tad-anyat tu
 sūkṣma-rūpaṁ śriyaṁ vinā

asuptaḥ supta iva ca
 mīlitākṣo ’bhavad dhariḥ
anyatrānādarād viṣṇau
 śrīś ca līneva kathyate
sūkṣmatvena harau sthānāl
 līnam anyad apīṣyate

After the annihilation of everything, the Supreme Lord, because of His sac-cid-ānanda-vigraha, remains in His original form, but since the other living entities have material bodies, the matter merges into matter, and the subtle form of the spirit soul remains within the body of the Lord. The Lord does not sleep, but the ordinary living entities remain asleep until the next creation. An unintelligent person thinks that the opulence of the Supreme Lord is nonexistent after the annihilation, but that is not a fact. The opulence of the Supreme Personality of Godhead remains as it is in the spiritual world; only in the material world is everything dissolved. Brahma-līna, merging into the Supreme Brahman, is not actual līna, or annihilation, for the subtle form remaining in the Brahman effulgence will return to the material world after the material creation and again assume a material form. This is described as bhūtvā bhūtvā pralīyate. When the material body is annihilated, the spirit soul remains in a subtle form, which later assumes another material body. This is true for the conditioned souls, but the Supreme Personality of Godhead remains eternally in His original consciousness and spiritual body.