This is just headcanon, but I don't think transfem Subaru would change her name to Natsumi.
Natsumi is a persona. But she's still a very genuine avenue for Subaru to explore femininity and the confidence that can be gained from it. And of course it's very easy to see how something like that could lead into realizing she's actually a girl too, but in a similar way that playing an idealized dnd character or drag performance would. Natsumi is Subaru's ideal self (canon description!) and that's still true either way.
But I think Subaru is still Subaru. Like, I think she'd go by the same name. It's gender-neutral (the canon Subaru genderbend uses the same name) for starters, but beyond that the name holds deep significance. Not just from a meta characterization standpoint, but because "Subaru" is the name of a star cluster, and that's the whole reason Subaru is into stars to begin with. I think that all versions of Subaru, cis or trans or genderbent or canon, like their name and would not choose to change it.
Additionally "Natsumi Schwartz" is the full name, and I highly doubt she'd ever change her family name especially. There is so much emphasis on Subaru's family and the fact that they can no longer be together. Carrying around the Natsuki surname matters. And I kinda don't think she'd go by "Natsumi Natsuki"
Idk I think Subaru's name just holds too much significance, both narratively and from a personal standpoint. That's why I can't really see any version of Subaru willingly and happily changing it.
Again, this is all headcanon so I don't think it's wrong to imagine a version where she changes her name to Natsumi or anything. It's just preference for me. But I also have a lot of different headcanons for Subaru anyway
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