Battler's identity

Axioms

• Battler says My name is Ushiromiya Battler.
• I am the golden witch Beatrice. And I opened this game in order to fight Ushiromiya Kinzo's grandchild, Ushiromiya Battler.
• Ushiromiya Battler's mother is Ushiromiya Asumu.
• My name is Ushiromiya Battler
• It was from Ushiromiya Asumu that Ushiromiya Battler is born.
• Battler prova a dire "It was from Ushiromiya Asumu that I was born" ma gli esce It was from Ushiromiya......nghu, ......?!
• You are not Ushiromiya Asumu's son.

Corollaries

There is one hint hidden away in Banquet that makes this riddle trivial to solve, while Kyrie is fighting one of the sevens stakes, she mentions that she and Battler's mother gave birth on the same day and that her son died.
With this red truth we can come to the conclusion that Asumu was actually the one who had a miscarriage.

Either Rudolf, Asumu, or both of them, secretly switched the newborns so that their marriage would be saved. Kyrie never discovered the switch, and we can't begin to guess how Beatrice learned of it, but it's a very clean solution.