Elephantonym: Ajax

ὅσον δὲ ἵππου Νισαίου μείζων ὁ Λιβυκὸς ἐλέφας, τοσοῦτον τῶν ἐκ Λιβύης οἱ Ἰνδοὶ μείζους.

περὶ δὲ ἡλικίας τοῦ ζῴου καὶ ὡς μακροβιώτατοι,εἴρηται μὲν καὶ ἑτέροις, ἐντυχεῖν δὲ καὶ οὗτοί φασιν ἐλέφαντι περὶ Τάξιλα μεγίστην τῶν ἐν Ἰνδοῖς πόλιν, ὃν μυρίζειν τε οἱ ἐπιχώριοι καὶ ταινιοῦν· εἶναι γὰρ δὴ τῶν πρὸς Ἀλέξανδρον ὑπὲρ Πώρου μεμαχημένων εἷς οὗτος, ὅν, ἐπειδὴ προθύμως ἐμεμάχητο, ἀνῆκεν ὁ Ἀλέξανδρος τῷ Ἡλίῳ. εἶναι δὲ αὐτῷ καὶ χρυσοῦ ἕλικας περὶ τοῖς εἴτ’ ὀδοῦσιν εἴτε κέρασι καὶ γράμματα ἐπ’ αὐτῶν Ἑλληνικὰ λέγοντα

ΑΛΕΞΑΝΔΡΟΣ Ο ΔΙΟΣ ΤΟΝ ΑΙΑΝΤΑ ΤΩΙ ΗΛΙΩΙ. [IEOG 400]

 ὄνομα γὰρ τοῦτο τῷ ἐλέφαντι ἔθετο μεγάλου ἀξιώσας μέγαν. 
ξυνεβάλοντο δὲ οἱ ἐπιχώριοι πεντήκοντα εἶναι καὶ τριακόσια ἔτη μετὰ τὴν μάχην οὔπω λέγοντες καὶ ὁπόσα γεγονὼς ἐμάχετο.

The Indian elephants are bigger than those from Libya by the same magnitude as the 'Libyc' are bigger than a Nisaean horse. As for the age of the animal and its extreme longevity, there has been discussion by others, but these men say that they encountered in Taxila, the largest city in India, an elephant which the natives perfumed and bedecked with ribbons. This indeed was one of these that had fought on the side of Porus against Alexander, and because it had fought valiantly Alexander dedicated it to Helios. It had gold bangles on its teeth or tusks, and on these were Greek letters saying:

Alexander, the son of Zeus, Ajax, to Helios.

For 'Ajax' was the name he bestowed on the elephant, thinking that a great creature deserved a great name. The natives reckoned that the battle had occurred three hundred and fifty years before [326 BCE], but did not say how old the animal was when it fought.
Flavius Philostratos, Life of Apollonios, 2.12.1-2. 

Observations:

• It is rare for mythological names to be bestowed on animals.
• We are told the reason for the choice of name.
• Ajax, son of Telamon, is known for his defensive role (ἔρκος Ἀχαίων, e.g. Il.6.5),  just as Porus' elephants carried armoured towers (2.12.1; cf. Q. Curtius Rufus 9.2: modo quis beluas efferentes moenium speciem, quis Hydaspem amnem, quis cetera auditu maiora quam vero sustinere posse credebat?).
• To my knowledge, this is the first example of an animal bearing an alphabetic indicator of its own name. Ivory tusks provided a unique opportunity for such inscriptions.

Ajax the elephant is mentioned again on the tour of Taxila.

ἱερὸν δὲ ἰδεῖν Ἡλίου φασίν, ᾧ ἀνεῖτο Αἴας ἐλέφας, καὶ ἀγάλματα Ἀλεξάνδρου χρυσᾶ καὶ Πώρου ἕτερα, χαλκοῦ δ’ ἦν ταῦτα μέλανος.

They say that they saw a shrine of Helios, to whom Ajax the elephant had been dedicated along with golden statues of Alexander and others of Porus - but these were of black bronze.

Flavius Philostratos, Life of Apollonios, 2.24

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Plurals of personal names: 2.33 (10,000 Achilleses and 30,000 Ajaxes would be insufficient) and 3.19 (men like Ajax and Nireus).