Mythical Inspirations behind Pyrrha's Name

Cassandra's Soul Chronicle in SoulCalibur III

SoulCalibur VI implies that Pyrrha was named after the wife of Deucalion, the man who survived the Great Flood. He's the Greek equivalent of biblical Noe:

And Prometheus had a son Deucalion. He reigning in the regions about Phthia, married Pyrrha, the daughter of Epimetheus and Pandora, the first woman fashioned by the gods. And when Zeus would destroy the men of the Bronze Age, Deucalion by the advice of Prometheus constructed a chest, and having stored it with provisions he embarked in it with Pyrrha. But Zeus by pouring heavy rain from heaven flooded the greater part of Greece, so that all men were destroyed, except a few who fled to the high mountains in the neighborhood. It was then that the mountains in Thessaly parted, and that all the world outside the Isthmus and Peloponnese was overwhelmed. But Deucalion, floating in the chest over the sea for nine days and as many nights, drifted to Parnassus, and there, when the rain ceased, he landed and sacrificed to Zeus, the god of Escape. And Zeus sent Hermes to him and allowed him to choose what he would, and he chose to get men. And at the bidding of Zeus he took up stones and threw them over his head, and the stones which Deucalion threw became men, and the stones which Pyrrha threw became women. Hence people were called metaphorically people (laos) from laas, “a stone.” And Deucalion had children by Pyrrha, first Hellen, whose father some say was Zeus, and second Amphictyon, who reigned over Attica after Cranaus; and third a daughter Protogenia, who became the mother of Aethlius by Zeus.

Apollodorus, Bibliotheca 1.7.2

That being said, I also found a different connection to Greek myths. Achilles allegedly used the name "Pyrrha" when crossdressing in order to hide at the court of Lycomedes, king of Scyros:

ACHILLES: When Thetis the Nereid knew that Achilles, the son she had borne to Peleus, would die if he went to attack Troy, she sent him to island of Scyros, entrusting him to King Lycomedes. He kept him among his virgin daughters in woman's attire under an assumed name. The girls called him Pyrrha, since he had tawny hair, and in Greek a redhead is called pyrrhos. When the Achaeans discovered that he was hidden there, they sent spokesmen to King Lycomedes to beg that he be sent to help the Danaan. The King denied that he was there, but gave them permission to search the palace. When they couldn't discover which one he was. Ulysses put women's trinkets in the fore-court of the palace, and among them a shield and a spear. He bade the trumpeter blow the trumpet all of a sudden, and called for clash of arms and shouting. Achilles, thinking the enemy was at hand, stripped off his woman's garb and seized shield and spear. In this way he was recognized and promised to the Argives his aid and his soldiers, the Myrmidons.

Hyginus, Fabulae 96

Given that the bit about Deucalion came many years after Pyrrha's name was first mentioned (in SoulCalibur II), I think that this is a much more likely reason why the writers originally decided on it. It rhymes nicely with "Patroklos," who was also mentioned for the first time in SoulCalibur II. The mythical Patroklos (or "Patroclus") was Achilles's childhood friend and most trusted fighting comrade. Achilles grieved for his death in the Illiad:

While he pondered thus in mind and heart, there drew nigh unto him the son of lordly Nestor, shedding hot tears, and spake the grievous tidings: "Woe is me, thou son of wise-hearted Peleus, full grievous is the tidings thou must hear, such as I would had never been. Low lies Patroclus, and around his corpse are they fighting—his naked corpse; but his armour is held by Hector of the flashing helm."

So spake he, and a black cloud of grief enwrapped Achilles, and with both his hands he took the dark dust and strewed it over his head and defiled his fair face, and on his fragrant tunic the black ashes fell. And himself in the dust lay outstretched, mighty in his mightiness, and with his own hands he tore and marred his hair. And the handmaidens, that Achilles and Patroclus had got them as booty, shrieked aloud in anguish of heart, and ran forth around wise-hearted Achilles, and all beat their breasts with their hands, and the knees of each one were loosed be-neath her. And over against them Antilochus wailed and shed tears, holding the hands of Achilles, that in his noble heart was moaning mightily; for he feared lest he should cut his throat asunder with the knife.

The Illiad 18.15–34

The bit about redheads also piqued my interest. Even though Pyrrha is blonde, she has freckles, which are a common trait among redheads.