As there is definite meaning of the names such as Lord Shiva, Indra, Vishnu etc. I want the meaning of
By the word Brahman, I mean with ultimate reality. (Though personally, I believe ultimate reality can't have any name- it is nameless)
The definition of Brahman is given in this chapter of the Taittiriya Upanishad:
yato va imani bhutani jayante ।
yena jatani jivanti ।
yatprayantyabhisaṃviśanti ।
tadvijijñasasva ।
tad brahmeti ।That from whence these beings are born, that by which, when born, they live, that into which they enter at their death, try to know that. That is Brahman.
This is the passage that Adhyaya 1 Pada 1 Sutra 2 of the Brahma Sutras is based on:
janmādyasya yataḥ
That (is Brahman) from which (are derived) the birth etc., of this (universe).
Now concerning the name , it has two meanings. As a name of Krishna, Vāsudeva refers to the fact that he is the son of Vasudeva. But Vāsudeva has been a name of Vishnu long before the time of Krishna. For instance, this chapter of the Valmiki Ramayana refers to Vishnu's incarnation Kapila as Vāsudeva. How is this possible? It's because Vaasudeva has another meaning. As a name of Vishnu, it refers to the fact that since Vishnu is the supreme Brahman, he is the one who dwells in all beings and in whom all beings dwell. Here is what this chapter of the Vishnu Purana:
The term Vāsudeva means that all beings abide in that supreme being, and that he abides in all beings
This chapter of the Udyoga Parva of the Mahabharata says much the same thing:
He is called Vasudeva in consequence of his enveloping all creatures with the screen of illusion, or of his glorious splendour, or of his being the support and resting-place of the gods. He is called Vishnu because of his all-pervading nature.
EDIT: You asked for the etymological meaning of these terms. The meaning of Vasudeva given in the Vishnu Purana and the Mahabharata is already an etymological meaning, as should be clear from seeing the original Sanskrit. Here is the Udyoga Parva verse I quoted above:
vasanāt sarvabhūtānāṃ vasutvād deva yonitaḥ
vāsudevas tato vedyo vṛṣatvād vṛṣṇir ucyate
So the word comes from the root "Vas", which means to dwell or abide.
And the etymological meaning of Brahman is given in this section of Adi Shankaracharya's Brahma Sutra Bhashya:
Brahman, which is all-knowing and endowed with all powers, whose essential nature is eternal purity, intelligence, and freedom, exists. For if we consider the derivation of the word 'Brahman,' from the root brih, 'to be great,' we at once understand that eternal purity, and so on, belong to Brahman.
The meaning of Brahman & Vasudeva according to Shreemad Bhagvat Purana.
वदन्ति तत्तत्वविदस्तत्वम् यज्ज्ञानमद्वयम् ।
ब्रह्मेति परमात्मेति भगवानिति शब्द्द्यते ॥ 11vadanti tat tattva-vidas
tattvaḿ yaj jñānam advayam
brahmeti paramātmeti
bhagavān iti śabdyateLearned transcendentalists who know the Absolute Truth call this nondual substance Brahman, Paramatma or Bhagavan.SB 1.2.11
Here is another translation by Motilal Banarsidass Publishers.
Those who possess the knowledge of truth (tattva) call the knowledge of non-duality as the Truth. It is also variously designated as Brahman ,Paramatma or Bhagvan.
So according to Bhagvata Brahman is non-dual entity ,which is absolute truth and that truth tatva is also called as Paramatma or Bhagvan.
यत्तत्सत्त्वगुणं स्वच्छं शान्तं भगवतः पदम् ।
यदाहुर्वासुदेवाख्यं चित्तं तन्महदात्मकम् ॥21॥yat tat sattva-guṇaḿ svacchaḿ
śāntaḿ bhagavataḥ padam
yad āhur vāsudevākhyaḿ
cittaḿ tan mahad-ātmakamThe mode of goodness, which is the clear, sober status of understanding the Personality of Godhead and which is generally called vasudeva, or consciousness, becomes manifest in the mahat-tattva.SB 3.26.21
Purport: The vāsudeva manifestation is called pure goodness, or śuddha-sattva. In the śuddha-sattva status there is no infringement of the other qualities, namely passion and ignorance. The vāsudeva stage is free from infringement by material desires and is the status in which one can understand the Supreme Personality of Godhead, or the objective which is described in the Bhagavad-gītā as adbhuta.
And here is description of Vasudeva from Motilal Banarsidass version.
(It is well known in agamas) that Mahat ,which is characterized by Satva-Guna ,Pure ,free from passion (like love hatred etc.) and the place of supreme lord is citta ,and it is called Vasudeva and is composed of Mahat-Tatva.
So Vasudeva is basically first among four Vyuha's who is supreme Mahat- Tatva ,which is of Satva Guna and seated within as the super soul in Lord’s expansion of 4 Vyuhas.
Brahman
First, when scripture usually (but not all the time, since the use of the feminine and masculine to a noun or pronoun is usually arbitrary) refers to Brahman in Sanskrit the neutral singular Brahma[n] is used. And most of the time when the masculine singular Brahmā is used it refers to Brahma[n] in His creative aspect as the four headed Creator. Sri Ramunja in his Sri-Bhasya to the Brahma Sutras says in his commentary to verse I.I.1 (translation by Swami Vireswarananda p 1):
The word ‘Brahman’ is derived from the root ‘brh’ which denotes greatness, and is therefore applicable to all objects which have the quality of greatness, but more aptly to that object which by nature and by qualities possesses this greatness to an infinite degree; hence the word ‘Brahman’ primarily denotes that supreme Person who is the abode of all auspicious qualities to an infinite degree and is free from all worldly taint. This supreme Person is the only Being the knowledge of whose real nature results in liberation.
Vāsudeva
In his Introduction to his translation of the Bhagavad Gita with the Commentary of Sankaracharya, Swami Gambhirananda writes on page xv:
…the Krsna of of the Mahabharata, otherwise known as Vāsudeva (son of Vasudeva and Devaki)…
And in a footnote to the above (p xv):
Vāsudeva is mentioned first in the Taittiriya Aranyaka, 10.1.6, ‘as a god together with Narayana and Visnu, apparently as mystically identical with them.’ (H. Jacobi, Encyclopedia of Religion and Ethics, vol. vii, p. 195.)
In agreement with this we see in the Mahanaryana Upanishad pp 45-6, verse I.29, translation by Swami Vimalananda:
May we know Narayana. For that, may we meditate on Vāsudeva. May Visnu impel us towards it.
And in his commentary on this verse he writes:
The Highest Person is here supplicated as Narayana, Vāsudeva and Visnu. Until and unless He impels the individual Soul, it cannot contemplate Him, and without contemplation on Him, His true nature cannot be understood. The etymological meanings of the three epithets are given at length in the bhasyas on the Gita and Visnusahasranama. Bhattabhaskara’s explanation of these words in the Visnugayatri is noteworthy. He derives Narayana thus: The term Nara, being derived from the root nr to lead, means the leader of all creation. Nara derived from the above word denotes his offsprings. Narayana therefore, is the effective cause of all creatures. Thus Narayana is Paramatman. He is called Vāsudeva in his immanent aspect, i.e., dwelling in all creatures as Antaryamin. The term Visnu implies His all-pervasiveness.
And at the end of his Introduction to the Gita, Sankara writes p 7 (Swami Gambhirananda translator):
This scripture, viz the Gita, while particularly revealing the twofold dharma having Liberation as its goal and the supreme Reality, Brahman, called Vāsudeva, as its subject matter,…
In the Gita Krishna refers to Himself several times as Vāsudeva. For example, in verse 7.19 the Lord says:
At the end of many births the man of Knowledge attains Me, (realizing) that Vāsudeva is all. Such a high-souled person is rare.
Thus, Brahman and Vāsudeva both refer to that same Supreme Godhead or Supreme Person of the Godhead.
Vasudeva is defined in Vishnu Purana last Book Chapter 5. It refers to the supreme being who resides in all beings.
He said, "He dwelleth internally in all beings, and all things dwell in him; and thence the lord Vásudeva is the creator and preserver of the world. "
Both the Vedic terms are used by the scripture for the Almighty. The former is used almost all the times for the impersonal supreme eternity(as per Bh.Gita 8.3), while the latter has defined some supreme personal eternal identity (Bh.Gita 7.19) , as well.
• Brahman: The Supreme Omnipresent Unknown, the Supreme Omnipotent Impersonal Infinity. As the Brahman (Vibhu-Brahman) only two eternal qualities are manifested, i.e. "vrihatam" or infinitely bigger eternity and "aksharam" or eternally indestructible.
Note that, the atman (jiva, soul) is also indestructible so it has been sometimes called as brahman (anu-brahman) in the Vedic literature.
Vedic Reference for the term "Brahman": https://asitis.com/8/3.html
• Vaasudeva: The Supreme Omnipresent, and Omnipotent Personal/Impersonal Cause. As Vaasudeva almost all the eternal features are manifested. Here the Vedic terms "Param-Brahman" and "Param-Atman" are also used interchangeably, as the Primeval Existence within the eternal Chaturavyuha (Vaasudeva-Sankarshana-Pradhyumana-Aniruddha).
In the eternal pastimes in mundane world, however, as a hidden eternal identity, Vaasudeva manifests as "the son of Vasudeva".
Vedic Reference for "Vaasudeva": https://vedabase.io/en/library/bg/7/19/
In Bh.Gita 14.27, it has been cleared by Him as "Vaasudeva" that He is also the basis of His impersonal "Brahman" revelation:
brahmano hi pratishthaham amritasyavyayasya cha shashvatasya cha dharmasya sukhasyaikantikasya cha
Translation: I am the basis of the formless Brahman, the immortal and imperishable, of eternal dharma, and of unending divine bliss.
