BB accessed the Moon Cell's Servant Archives, chose goddesses compatible with the Ego from them, and reproduced the data. Alter Egos came into existence as complexes of goddesses.
Passionlip is made of three goddesses.
The first is the goddess of beauty from Hindu mythology, Parvati. A goddess who loves her husband, the god of destruction Shiva, with blind devotion.
The second is the goddess of war, Durga. Considered a facet of Parvati, Durga possess ten weapons given to her as divine gifts. Passionlip's giant claws are an incarnation of those ten swords.
The third is a goddess of war from Scandinavia, Brynhildr. Unable to be tied to the hero she loved, this queen called destruction to her though her grief. In Wagner's opera, she was rendered as Brünnhilde, who appears as a valkyrie (war maiden) who escorts the souls of the departed to Valhalla. It goes without saying that the circumstances of this work led to a tragedy where she despaired over love and raised her hands against her beloved.

Fate/EXTRA CCC Passionlip (Alter Ego) Matrix