Alright, it should be something in the basic information that is written to battle data... Instead of the normal naming, it is copied from the basic data however. Where does the editor draw its name to save? In the out-of-battle data and the very first byte of in-battle data the name is proceeded by an 8X so 81 is Cecil, 82 is Kain, etc.
It should be noted that the editor does not edit either of these, but seems to edit something else, somewhere else to show it on the formation screen.

0x7AB00 is where it begins, starting with Dark Knight Cecil as you are aware these are the initial stats. it does not seem now that the first half of the byte is the name. Only the second half. I cannot say what the first half does, but the second half is the naming used in battle.

2 : The Editor can actually edit this already, you have the listing under "Initial Actor" but as far as I can gather it is purely the name byte used in-battle.

3: Nope, I'm wrong. That also changes the commands for the character and their ID... and when they're removed... so it's clearly not just... name. Hmm...