Name issues can be very tricky. there is not necessarily a right and wrong answer. Particularly if your are from certain countries, the name discrepancy can be a problem on the security check. You should be able to straighten the mess out with the naturalization process, but I strongly recommend consulting with a lawyer to determine which name should be listed, what should be an aka and what explanation/documentation needs to be provided.
This is going to be very fact specific. I would suggest sitting down with an immigration lawyer to discuss this matter in depth.
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