You get the oath ceremony the same day as the interview? Wow! They don't do that here. Anyway, yes, it is too late to change your name through the citizenship process. You can still go to court and file for a name change.
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No you cannot. You will have to apply for it through the court.
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I t is too late. You should have told them during the interview, in which case it would have taken much longer for you to receive the certificate. you can always consult a lawyer if you have more questions.
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