I said it as a joke at first but this comic makes a lot more sense (and also just becomes a lot funnier) if she's trans and baffled by how the Japanese are too stupid to realize she's outed herself when she has to stamp her deadname on every document.
In english speaking countries there's almost no instances of 'baptismal names' nowadays - it's just your legal forename, because most Christians nowadays are baptized at birth or close enough to it. Even for converts I don't think any denominations of Christianity urge you to take up a new name, those that do usually do so out of their own will and replace their forename. There's a reason "Christian name" is just another way of saying first name in the anglosphere. It's such a given we don't even realize it's a thing anymore.
Ergo if her 'baptismal name' is Elijah, then in England she was born as Elijah. That's not a mistake you can make even if your english skills are poor. So it obviously makes no sense...unless, hilariously, she was born biologically male, transitioned, and chose 'Yui' as her new name but was still stuck with "Elijah" on her passport.