It's like your favorite color is blue and the person you love most has blue eyes. If you stop liking the color blue, it doesn't change the eye color of your favorite person.
A death name was still your name at birth.
Changing it is okay but it doesnt erase that fact.
I think the name wouldn't show up on the other person until they embraced their real identity and the new name. It's not like the names have anything to do with your government name. It's more about identity. So I definitely think it'll be the new name that will show up.
At least that's what I'd like to think personally. It would be too sad if people had fated partners with the name they don't identify with, tattooed on their bodies forever.
i wonder how this name thing works for trans people with deadnames