Anne only makes some short appearances within the games, but holds special meaning. She is Ben Hyuga's mysterious Russian wife, and the mother of Yuri Hyuga.
"The main character's mother. A beautiful Russian woman. Many details of her life remain a mystery. Dehuai's demons took her life before her son's eyes."
Not long after her husband was sent to fight the warlock Dehuai in Shanghai, that very same warlock sent demons to attack and kill her and Yuri.
Sadly, she died during the siege, an event which caused her son's powers as a Harmonixer to come to light as Yuri raged and killed the demons in turn.
She is mentioned in passing in Shadow Hearts: Covenant, most notably in an accessory known as Anne's Cross, which is only wearable by Karin Koenig.
As revealed in the ending of Shadow Hearts: Covenant, Anne Hyuga is actually Karin Koenig, sent back in time after defeating Susano-O. Her unintended trip back in time causes her to encounter Jinpachiro Hyuga, using her alias as "Anne" given to her by Princess Anastasia Romanov as a way to hide her German heritage, eventually giving birth to Yuri.
This makes her existence a predestination paradox and Yuri's an ontological paradox.