Oh you absolutely have to register new versions of personas you already have. If there is a level 15 Persona with bufu in your compendium and you capture a level 20 version with bufula then you need to register it so that it overwrites your low level Persona.
Similarly if you have a level 15 Persona in the compendium and then level it up via gameplay to level 20 then you need to manually register that to overwrite the low level version as well. On the other hand if you gain a new persona via fusion it's automatically registered as well.
The question is what if it's a Persona that's not in your compendium and you capture it via fights? I am pretty damn sure that you need to manually register it in this case.
Ah ok, I get what you're saying.