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So my theory for the trademarks and registrations is that she commissioned a design so close to Gura, along with her logo and stream assests, that she's afraid of Cover potentially coming after her because the similarities will be higher than other members who have left the company. And so maybe she believes that filing trademarks would help dissuade any potential future legal disputes over branding and whatnot.
If that's the case, I'm not really sure it would help her legally, and it may in fact even end up having the opposite effect, causing a judge to determine she deliberately tried to infringe on Cover's IP and then attempt to shield herself by trademarking designs that she knew violated any contract she may have signed with them.
I'm not a lawyer though, and I really only studied copyright law a little bit a few years ago during the whole youtube fair use debacle, which is different from patent and corporate trademark law, so I might be totally wrong. Either way, Cover hasn't gone after any of the others for making "legally distinct" versions of their hololive personas, not even Rushia, so she probably doesn't have anything to worry about. At least I hope not.
I just can't really think of any other reason as to why she'd be so aggressive is pursuing these filings and registrations when it's mostly totally unnecessary for an indie vtuber. The only other reason to do it would be if she planned on going after anyone making and selling small amounts of fan merch or derivative works, like at artist alleys or fanmade projects, but that doesn't sound like something she'd do.
I definitely don't think it was her idea either. She's definitely working with someone, either a manager or a lawyer that suggested it.