[chronotrig]

This whole thing about 'what is someone's name' has me a bit edgy. Names are important in almost all magic-related fantasies, but we don't know the rules for how people are named in Umineko.

Spoiler for ep4:

And to make things more interesting, Beato only ever uses the family names for Kumasawa, Gohda and Nanjo. Now that we have another Kumasawa and Nanjo (their sons) with tachi-e's, that gives us some interesting leeway.

And even more odd is the fact that Kanon is Kanon's name. Think about it. It was a name he was given when he was employed, and he has another name. So we know:
1. People can be given names by other people or groups after they are born, and
2. people can have multiple names, unless Kanon's original name is actually no longer his name.

So if you want to argue that Ange has another name, Battler, then there's nothing that we've seen so far that proves you wrong.
I'm not quite sure if that helps wrap up any mysteries though.