Who is called a dwija?

dvija indicates twice born.

All types of spiritual concepts in sanatana dharma aka Hindu dharma can be traced back to Rig Veda. And, the term dvija can be found in Rig veda, but used in a different connotation.

The only issue is, the concepts of Rig Veda should be understood in an esoteric sense only, but not in a literal sense.

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We have to remember that according to the Rig Vedic rishies, the term dvija does indicate a person (man/woman), who after born as human being (first birth) , does spiritual practices, conquers his senses and pleasures, becomes enlightened or gets SELF REALISATION (2nd birth).

Indra/Agni/vishnu, etc, are the different names of the same God, by the which the Rig Vedic rishies used to address the SUPREME POWER.

And, they used to treat the God as the father also.

Rig Veda 7.32.3

रायस्कामो वज्रहस्तं सुदक्षिणं पुत्रो न पितरं हुवे ॥
rāyaskāmo vajrahastaṃ sudakṣiṇam putro na pitaraṃ huve ||

English translation:

“Desirous of riches (enlightenment) , I call upon the benevolent wielder of the thunderbolt (Indra), as a son upon a father.”

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When the spiritual aspirant reaches the highest level, ONE finds oneself, as reborn as the splendorous SUN.

Rig Veda 8.6.10

अहमिद्धि पितुष्परि मेधामृतस्य जग्रभ । अहं सूर्य इवाजनि ॥
aham id dhi pituṣ pari medhām ṛtasya jagrabha | ahaṃ sūrya ivājani ||

English translation:

“I have verily acquired the favour of the true protector (Indra); I have re-born (bright) as the sun.”

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After this re-birth, ONE becomes a dvija.

Thus, it is the highest spiritual stage attained, after undergoing rigorous practices, as in the case of Shri Ramana Maharshi.

It is not a status to be conferred upon a person, upon who have undergone upanayana ritual.

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Rig Veda 10.61.19

इयं मे नाभिरिह मे सधस्थमिमे मे देवा अयमस्मि सर्वः । 

द्विजा अह प्रथमजा ऋतस्येदं धेनुरदुहज्जायमाना ॥

iyam me nābhir iha me sadhastham ime me devā ayam asmi sarvaḥ | 

dvijā aha prathamajā ṛtasyedaṃ dhenur aduhaj jāyamānā ||

“This, here, is my navel, and here is my seat. These gods here are mine, and here am I—the whole— having two births, first born of truth. This (earth?) here did the cow give as her milk as she was being born.”

The rishi of this Rik is explaining his experience. After enlightenment, he experiences after the two births, he had become ONE with the ETERNAL DIVINITY aka the God, who is called the first born or prathamajā and found that he had become the source of everything.

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However, by the time Manu Smriti was composed, the concept of dvija was shifted to indicate a status to be conferred upon a person, upon who have undergone upanayana ritual.

Manusmriti Verse 2.27

गार्भैर्होमैर्जातकर्मचौडमौञ्जीनिबन्धनैः ।
बैजिकं गार्भिकं चैनं द्विजानामपमृज्यते ॥ २७ ॥

gārbhairhomairjātakarmacauḍamauñjīnibandhanaiḥ |
baijikaṃ gārbhikaṃ cainaṃ dvijānāmapamṛjyate || 27 ||

Of twice-born men the taint of seed and womb is removed by the ‘Libations in connection with Pregnancy’ and by ‘Jātakarman’ (Rites attendant upon birth), ‘Chauḍa’ (Tonsure) and ‘Mauñjībandhana’ (Tying of the grass-girdle). (27)

Manusmriti Verse 2.170

तत्र यद् ब्रह्मजन्मास्य मौञ्जीबन्धनचिह्नितम् ।
तत्रास्य माता सावित्री पिता त्वाचार्य उच्यते ॥ १७० ॥

tatra yad brahmajanmāsya mauñjībandhanacihnitam |
tatrāsya mātā sāvitrī pitā tvācārya ucyate || 170 ||

Among these, at that Brahmic birth which is. marked by the tying of the girdle, the Sāvitrī has been declared to be his “Mother,” and the Teacher his “Father.”—(170)

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By the time Ramayana was composed (I am not talking about occurrence of Ramayana here), dwija was being used to indicate brAhmanas only.

The ascetic boy, being hit by the arrow of Dasaratha, says that he was born to a Vysya and to a Sudra woman:

न द्विजातिर् अहम् राजन् मा भूत् ते मनसो व्यथा | शूद्रायाम् अस्मि वैश्येन जातः जन पद अधिप || २-६३-५३

'O, king the ruler of the country! I am not a Brahmana. Let there be no agony in your mind. I am born through a Sudra woman by a Vysya.

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At a still later period, the word dwija used to refer brAhmana, kshatriya and Vysya also, after undergoing upanayana ceremony.