It isn't confusing at all! They would forget that they're named ____, but because it would be unreasonable to have characters forget the name of an entire country, they just become unable to recognize it as their name.
To use America as an example: Let's say that he was given the work name "Teddy." Teddy has a run-in with some characters from the US, and they're able to introduce themselves as Americans, but Teddy doesn't recognize that name as being his, because he's forgotten it.
However, considering what a mess that is, it's totally logical to assume that a country character, particularly one with a lot of its citizens in Koriko, would regain their name quickly.
I hope that makes sense! Please don't be afraid to ask me to clarify.
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To use America as an example: Let's say that he was given the work name "Teddy." Teddy has a run-in with some characters from the US, and they're able to introduce themselves as Americans, but Teddy doesn't recognize that name as being his, because he's forgotten it.
However, considering what a mess that is, it's totally logical to assume that a country character, particularly one with a lot of its citizens in Koriko, would regain their name quickly.
I hope that makes sense! Please don't be afraid to ask me to clarify.