Alter Ego

The Alter Egos are alternate personalities separated from the ego of BB. Indeed, Alter Egos.
Alter Egos are a group of high-level AI’s created by BB in CCC.
These girls who were created from BB’s emotions each have a soul, and are active in the cyber world as entities completely separate from BB.
Creating a soul is not a difficult task for Moon Cell, this is because the design and structure of souls has already been discovered. The problem lies in whether the “container” known as a soul can contain self-awareness.
The Alter Egos were all created as incomplete copies, so in order to account for this flaw they were each bestowed with independent self-awareness separate from BB’s.
Each Alter Ego inherits a single emotion from their progenitor BB. This is why Passionlip is embodied with despair, and Meltlilith is a disciple of destruction.

To digress, in the original design plans for CCC there were 5 Alter Egos, and during development they were called “The Sakura Five.” Passionlip and Meltlilith are the two victorious Sakuras of the five who survived the cruel life-or-death competition to the end1, before the release of CCC.

Translator's Notes
  1. ^ In order to make it into the game.
Fate/EXTRA Material: Encyclopedia of Fate/EXTRA