Q: If all characters share the same familiar, will the player be able to name them differently for each character?
This.
That's the reason why the account sharing with familiars wouldn't work. It would make more sense if we could remove them from our familiar book and place them back into our Use Inventory for other purposes. Maybe the draw back could be that we can't remove them entirely from the codex, but only decrease their vitality to default when they were first registered (as in back to 1 orb). So for example, if you don't have two or more vitality registered to the familiar, you can't convert the second or third vitality orb it into a card to place back into your Use inventory.
As for the familiar renaming, we could spend a certain amount of mesos to rename our familiars to something new. I've always pictured the renaming system to be similar to the medal reissuing system, where the fee adds an extra 0 to the sum the more you try to reissue for a medal you want back, and then stop at a certain limit.
Can we get a familiar name changing system? I don't like the idea of a naming a familiar and its name stays permanent. I would love it if you guys added the option to change our familiar names to something we can be more satisfied with.