Whose name is this? - Page 23

Correct! In Mahābhārata, it is Pradyumna who is called Rukmiṇinandana three times when Kṛṣṇa narrates Pradyumna's battle with Śālva.

69. Who was known as Bhaimi?

Ghatotkacha

I also found Damayanti is Bhima's daughter, married to Nala. Not sure if it's the same Bhima from Mahabharat or a different one.

Correct! Bhīma's son Ghaṭotkaca is Bhaimi.

The story of Nala and Damayantī is told in Āraṇyakaparvan, in which they are contemporaries of Ṛtuparṇa, an ancestor of Rāma Dāśarathi. Damayantī is often called Bhaimī because her father named Bhīma is the king of Vidarbha, and obviously different from Bhīma Pāṇḍava.

70. Who is called Vajradharātmaja?

70. Arjun?

Attempting this without Google 😆 solely cuz I think Vajradhara means wielder of Vajra which is Indra and Atmaja is son.

Correct!

71. Who was known as Pārvatīya?

Parvati putra? Kartikeya and Ganesha?

No; Pārvatīya is a geographical name that is repeatedly used along with the personal name of an important character in the action of Mahābhārata.

Not sure which of this fits

Parvatiya (पार्वतीय) is mentioned in Mahabharata (I.61.38), (VI.10.56),(VIII.30.79),(VIII.51.19).

Adi Parva, Mahabharata/Mahabharata Book I Chapter 61 mentions.... Kratha, was born on earth as the royal sage Parvateya of form resplendent like a golden mountain[21]..... The mighty Danava known by the name of Kukshi became on earth as Parvatiya from his brightness as of a golden mountain.

Bhisma Parva, Mahabharata/Book VI Chapter 10 describes geography and provinces of Bharatavarsha. Parvatiya is mentioned in the the list of Provinces in verse (VI.10.56)....."the Oshtras, the Paundras, the Sairandhras, and the Parvatiyas and Marisha..." [22]

Karna Parva/Mahabharata Book VIII Chapter 30 blames the Vahikas and Madrakas. Parvatiya are mentioned in verse (VIII.30.79)... The Magadhas are comprehenders of signs; the Koshalas comprehend from what they see; the Kurus and the Panchalas comprehend from a half-uttered speech; the Salwas cannot comprehend till the whole speech is uttered. The Mountaineers (Parvatiya), like the Sivis, are very stupid. [23]

Karna Parva/Mahabharata Book VIII Chapter 51 ... Describes terrible massacre on seventeenth day of War... Parvatiya are mentioned in verse (VIII.51.19) fighting for Kurus ...."the Andhrakas, the Pulindas, the Kiratas of fierce prowess, the Mlecchas, the Mountaineers, and the races hailing from the sea-side, all endued with great wrath and great might, delighting in battle and armed with maces, these all--united with the Kurus and fighting wrathfully for Duryodhana's sake were incapable of being vanquished in battle by anybody else save thee"[24]

I commend your research effort.

The geographical term Pārvatīya means "from the mountainous regions" and appears alongside terms for Easterners, Westerners, Southerners, and Northerners.

However, I am looking for the name of one particular individual who is repeatedly called a Pārvatīya.

That individual did not feature on page 1 of Google search 🤣 I'll look for it later 😆